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This paper investigates the aperiodic sampling stabilisation problem for a class of switched linear systems under asynchronous switching. Based on a novel dynamic sampling rule, a sampling-point-based partition-dependent discontinuous Lyapunov functions control approach are developed to make the considered closed-loop switched systems be globally asymptotically stable. Compared with the existing results, the proposed control method permits frequent switching in a sampling interval for subsystems. But the frequent information transmission to the matched controllers and the negative effect of long asynchronous running on system performance can be nicely handled in this paper. Moreover, the partitioned Lyapunov functions are allowed to increase in some segments of the synchronous operating intervals. Tighter synchronous duration and switching number which are determined by more than affine functions make the switching signal more flexible. Finally, simulation analyses of two examples show the advantages of the developed control strategy. [ABSTRACT FROM AUTHOR]

The problem of $ L_1 $ L 1 output tracking control of positive linear systems in finite time is addressed in this paper. By constructing a linear copositive Lyapunov–Krasovskii functional, some sufficient conditions are achieved to ensure that the states are finite-time bounded and the measurement outputs have $ L_1- $ L 1 − gain performance for given systems, respectively. Next, a state feedback controller is designed to ensure that the output signals of the tracking system can effectively trace the specified signals of reference model with finite-time boundedness and $ L_1 $ L 1 -gain performance. Finally, an example is given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The quotient space method provides a novel idea for modelling the transient dynamics of dimension-varying control systems. This paper investigates the realisation problem of the transient dynamics of dimension-varying control systems. By revealing the structure of the controllable subspace for the linear system on quotient space, we propose the condition for the realisation of the transient dynamics of dimension-varying control systems, based on which a new scheme for modelling the transient dynamics is given. Moreover, the proposed scheme justifies the existing result for the strategy for modelling the transient dynamics. A numeric example is given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a novel ensemble learning-based adaptive stochastic model predictive control (SMPC) algorithm for constrained linear systems with unknown nonlinear terms and random disturbances. The ensemble network combining a feedforward neural network and a Bayesian network is used to offline learn the nonlinear dynamics and disturbance distribution parameters. Then, the mixed-tube scheme is designed to cope with input constraints and state chance constraints while decreasing computational demands and conservativeness. The reliability of the stochastic tube is guaranteed using the Hoeffding inequality-based verification mechanism, which results in a chance constraint with double probabilities. The feasibility and exponential stability of the SMPC are rigorously proven. A numerical example verifies the merits of the proposed algorithm in terms of the control performance and the feasible domain. [ABSTRACT FROM AUTHOR]

This paper deals with generalised Caputo fractional proportional linear time-invariant systems in a finite-dimensional space. The Laplace transformation method ensures the analytical solution of the desired fractional linear time-invariant systems. The present article presents the necessary and sufficient conditions for controllability and observability of the generalised Caputo proportional fractional linear time-invariant systems. These two properties can play a more fundamental role in system analysis before controller and observer designs are engaged. Moreover, we have acquired the criterion for generalised Caputo proportional fractional linear time-invariant systems as Kalman rank conditions. Some numerical examples are presented to show the applicability of the paper to demonstrate our findings. Finally, we derive the necessary and sufficient controllability conditions for the generalised Caputo proportional fractional-order nonlinear Chua's electric circuit. [ABSTRACT FROM AUTHOR]

In this paper we propose a robust output feedback control scheme for constant reference tracking in uncertain linear systems subject to state and control constraints. First, we establish conditions under which a polyhedral set is Output Feedback Controlled Invariant with respect to a linear system subject to polytopic uncertainties, i.e. a set guaranteeing robust constraint satisfaction via output feedback. Then, we build a dynamic output feedback controller for the uncertain model based on set-membership observers, allowing the reduction of the set of possible states consistent with the measurements. Finally, to reduce the tracking error, we propose a model update procedure that adjusts the nominal model used for tracking to the output measurements. Numerical experiments illustrate the ability of the proposed controller to achieve reference tracking with reduced offset for the uncertain systems under consideration. To the best of our knowledge, it is one of the first works that addresses constant reference tracking in uncertain linear systems under constraints with output feedback. [ABSTRACT FROM AUTHOR]

This paper considers reachable set estimation for discrete-time linear time-delay systems. With the assumption that the unknown initial condition and disturbances are bounded by zonotopes, three zonotope-based methods are proposed to estimate the real-time reachable sets. We find that the couplings in the time-delay systems lead to conservative estimation results and propose a reachable set estimation method based on state augmentation. The augmentation-based method can reduce the conservatisms caused by the time-delay and achieve more accurate reachable set estimation. Simulation results demonstrate the performances of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider the energy-to-peak filtering issue for a class of linear parameter-varying (LPV) systems with time delays subject to certain communication regulation under which only one sensor is allowed to transmit its measurement data at each transmission instant. The data communication is regulated by the random access protocol (RAP) for the purpose of avoiding data collisions. The main purpose of this paper is to design an LPV filter such that the resultant filtering error system is asymptotically stable and also satisfies the prescribed l 2 - l ∞ performance in the mean square. Taking into account both the LPV nature and the possible gain perturbations, a parameter-dependent resilient filter is constructed according to the plant dynamics and scheduling behaviour of the RAP. The desired filter gain matrices are obtained by solving a set of linear matrix inequalities. Finally, a simulation example is given to validate the effectiveness and correctness of the filter design scheme. [ABSTRACT FROM AUTHOR]

The problem of complete controllability is addressed for a class of switched time-varying impulsive systems under multiple input delays. Several controllability criteria are obtained with the aid of algebraic and geometric tools. Firstly, the explicit expression of solution on every impulsive interval for such systems is derived by mathematical induction and variation of parameters. Then, complete controllability is investigated for the underlying system based on the solution established. Specifically, the new necessary or/and sufficient algebraic controllability conditions are obtained without assuming that all impulse-dependent matrices are non-singular. In addition, the geometric criteria with regard to the constant matrices are further discussed when the considered system reduces to a time-invariant case. Finally, numerical examples are worked out to demonstrate the controllability tests derived in this paper. It is shown that the existence of the delayed term will potentially affect the controllability of the studied system. In contrast to the existing literatures, the criteria derived in this paper removing some constrained assumptions have less conservatism and can be used to verify the controllability of a more general linear hybrid system. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive finite-time tracking problem for nonlinear sandwich systems with dead-zone nonlinearity and full state constraints. The existence of the non-smooth dead-zone nonlinearity between the subsystems of the sandwich system makes the controller design as a challenging task. In this paper, a novel adaptive backstepping controller is proposed by employing the finite-time stability theorem and based on the barrier Lyapunov functions and finite-time command filters. The proposed controller guarantees the output tracking of the specified time-varying reference signal with the sufficiently small bounded tracking error in a finite-time. Moreover, all states of the controlled system are confined to predefined compact sets. To verify the theoretical achievements and show the applicability of the proposed method, simulation results are provided for both numerical and practical examples. [ABSTRACT FROM AUTHOR]

This paper is to investigate the linear minimum mean square error estimation for Markovian jump linear system subject to unknown Markov chains, multi-channel mode and observation delays, and packet losses. The reorganisation method is employed to convert the delayed measurement system into an equivalent delay-free one and a new state variable is introduced, by which the original state estimation with transmission delays and data losses is transformed into the new state estimation for the reorganised delay-free system with jumping parameters and multiplicative noises. The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations. Then the original state estimation will be obtained via the jumping property. Finally, we show that the difference Riccati equations converge to a set of generalised algebraic Riccati equations under appropriate assumptions, which result in an optimal stationary filter. [ABSTRACT FROM AUTHOR]

This paper proposes a new adaptive gain robust model-following/tracking controller for a class of uncertain linear systems. The proposed adaptive gain robust controller is composed of state feedback laws with fixed gains, feedfoward inputs for the reference model and nonlinear compensation inputs with adjustable time-varying parameters. Moreover, the proposed control strategy can achieve good transient performance and avoid the excessive control input by means of the design parameter. In this paper, linear matrix inequality-based sufficient conditions for the existence of the proposed adaptive gain controller are given, and two design strategies are presented. Finally, simple illustrative examples are included to show the effectiveness of the proposed adaptive gain robust controller. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the semi-global asymptotic stabilisation of fractional-order (FO) linear systems subject to actuator saturation by output feedback. To solve the problem, a family of observer-based linear output feedback laws, parameterised in a positive scalar, is proposed by means of the low gain feedback design technique. The design applies to FO linear systems that are stabilisable and detectable, but not exponentially unstable. For such an FO system under the proposed observer-based linear low gain output feedback, the peak value of the control input for a given initial condition can be made arbitrarily small to avoid actuator saturation by decreasing the value of the parameter towards zero and thus semi-global asymptotic stabilisation is achieved. To obtain these results, we establish the properties of low gain feedback, derive asymptotic expansions and the bounds of high-order derivatives of the Mittag-Leffler (ML) functions to estimate the state responses of FO linear systems, and explicitly construct a Hermitian matrix to satisfy a linear matrix inequality (LMI) stability condition for FO linear systems. The results in this paper extend the corresponding results for integer-order (IO) linear systems. [ABSTRACT FROM AUTHOR]

In this paper, the mixed H 2 / H ∞ guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the D -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed H 2 / H ∞ guaranteed cost minimisation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the observability of linear stochastic impulsive systems with multiplicative noise. The concept of 2pth moment observability is first introduced. Then, to explore the moment observability, a deterministic expanded system is established for the linear stochastic impulsive systems by the generalised H -representation technique. It shows that the linear stochastic impulsive system is 2pth moment observability if and only if the expanded system is completely observable. Subsequently, a series of algebraic criteria and geometric criteria for 2pth moment observability of linear stochastic impulsive systems are established by analysing the solution of the expanded system. The impulsive observer-based stabilisation problem for linear stochastic systems is further studied based on these observability criteria. Finally, two numerical examples illustrate the proposed theoretical results. [ABSTRACT FROM AUTHOR]

The impulse response function (IRF) identification of linear mechanical systems is important in many engineering applications. This paper proposes a novel IRF identification method of linear systems based on Kautz basis expansion with multiple poles. In order to reduce the parameters to be identified, the IRF is expanded in terms of orthogonal Kautz functions with multiple poles, and the poles in Kautz functions should be optimised. This allows the identification of IRF for linear mechanical systems operated under more than one mode, such as systems under the white noise excitation or the swept frequency excitation with a wide range of frequency, and can improve the identification accuracy. Furthermore, based on the backpropagation through-time technique and the expectation maximisation algorithm, a pole optimisation algorithm is presented in this paper. The simulation studies verify the effectiveness of the proposed IRF identification method. [ABSTRACT FROM AUTHOR]

We consider in this paper the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises (MJLS-mn for short). Our objective is to present an optimal policy for the problem of maximising the system's total expected output over a finite-time horizon while restricting the weighted sum of its variance to a pre-specified upper-bound value. We obtain explicit conditions for the existence of an optimal control law for this problem as well as an algorithm for obtaining it, extending previous results in the literature. The paper is concluded by applying our results to a portfolio selection problem subject to regime switching. [ABSTRACT FROM AUTHOR]

The problem of robust stabilisation for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown and an improved adaptation law with σ − modification is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds, we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes in the presence of multiple delayed state perturbations is globally uniformly practically exponentially stable. Finally, a numerical example is given to demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

Delay and actuator saturation are inevitable in practical control engineering, which may lead to system performance degradation, or even divergence of controlled variables. Combination of Smith predictor (SP) and model recovery anti-windup method is an effective solution to anti-windup synthesis for linear delayed systems, but model-dependent property brings obstacles for the application and promotion. To overcome such a difficulty, a few-shot data-driven approach has been proposed in this paper, and operating data are collected to simultaneously tune feedback controller parameters and estimate internal model applied in SP. Subsequently, the anti-windup compensator is constructed with the estimated model and compensator gain is calculated by using the Lyapunov equation. Finally, the effectiveness of the proposed method is verified through simulations that implemented three typical processes in engineering. [ABSTRACT FROM AUTHOR]

In this paper, a class of nonlinear interconnected systems with matched and unmatched uncertainties is considered. The isolated subsystem dynamics are described by linear systems with nonlinear components. The matched uncertainties and unmatched unknown interconnection terms are assumed to be bounded by known nonlinear functions. Based on sliding mode techniques, a state feedback decentralised control scheme is proposed such that the outputs of the controlled interconnected system track given desired signals uniformly ultimately. The desired reference signals are allowed to be time-varying. Using appropriate transformations, the considered system is transformed into a new interconnected system with an appropriate structure to facilitate the sliding surface design and the decentralised control design. A set of conditions is proposed to guarantee that the designed controller drives the tracking errors onto the sliding surface. The sliding motion exhibited by the error dynamics is uniformly ultimately bounded. The developed results are applied to a river quality control problem. Simulation results show that the proposed decentralised control strategy is effective and feasible. [ABSTRACT FROM AUTHOR]

In this paper, the practical mean-square scaled-consensus problem of multiagent systems is studied. Higher-order general linear dynamics is investigated, where all agents are subject to faults or denial of service attacks (DoS). The considered network comprises agents taking quantised states under undirected communication channels. Different from the existing works, no strict conditions have been imposed on the eigenvalues of the agents' state matrix. First, we propose a distributed scaled-consensus protocol that utilises a probabilistic quantisation algorithm. Second, scaled-disagreement analysis is provided via mean-square stability methodology. Finally, sufficient conditions in terms of linear matrix inequalities are presented in order to obtain scaled-consensus gain for both leaderless and leader–follower cases. The presented theoretical results are examined through two simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies fault detection problem in the finite-frequency domain for linear systems with parameter uncertainties. We design an fault detection observer to generate residual that is robust against disturbance and sensitive to a fault. In the design, we use the finite-frequency performance index to measure fault sensitivity and introduce performance index to measure the effect of disturbance on residual. The obtained fault detection observer exhibits a peak-to-peak disturbance attenuation performance, which provides a time-varying threshold for residual evaluation. Therefore the proposed design method integrates residual generation and threshold calculation together. To facilitate the observer design process, sufficient conditions of the proposed fault detection observer are formulated as a set of linear matrix inequalities. Numerical simulations are given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of reliable load frequency control design of an uncertain multi-area power system with constant time delays and disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which are described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov-Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the multi-area power system not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique. [ABSTRACT FROM AUTHOR]

Control of time-varying systems has become increasingly popular in recent years, as various domains such as aviation, automobile and manufacturing industries require a quick and precise response in the presence of uncertainties. Adaptive control, a popular strategy is used to control systems with unknown or time-varying properties. Classic adaptive control is insufficient to cope with time-varying parameters to produce desired results with minimal parametric error. Furthermore, for these strategies to work, identification model must be initialised closer to the plant. Else the transient response of the plant is likely to grow unbounded. This paper mainly concentrates on employing adaptive control for a type of linear time-invariant (LTI) and linear time-varying (LTV) systems. The time variations in LTV plant parameters are either slow, rapid or fast. This research in turn proposes a two-stage adaptive scheme which swiftly determines the compact region in which plant parameters reside. This method in turn ensures atleast one model to be initialised closer to the plant which significantly reduces parametric estimation error. The uniform boundedness of identification error, tracking error as well as the parametric error of LTI and LTV systems, are deduced. Sufficient examples are also considered to demonstrate the efficacy of the proposed two-stage scheme. [ABSTRACT FROM AUTHOR]

In this paper, a high-gain interval observer (HGIO) for a class of partially linear continuous-time systems with sampled measured outputs in the presence of bounded noise and additive disturbances is proposed. The design of the HGIO is formulated in the Linear Matrix Inequality (LMI) framework. The gain of the HGIO is designed to satisfy the cooperative property using a time-varying change of coordinates based on pole placement in separate LMI regions. Moreover, a procedure for designing the HGIO gain to minimise the effect of the noise and disturbance in the estimation is provided. The stability of the proposed HGIO is also guaranteed. The proposed approach is assessed in simulation using a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the optimal tracking problem for discrete-time linear systems with multiple delays is studied without system dynamics. It is known that the total state of a system without specific dynamic characteristics is hard to be measured, unless such a system is equipped with massive sensors, which, however, may lead to an increase in cost and complexity for analysing. To deal with this problem and avoid adverse effects caused by using system state information, a new data-driven value iteration (DDVI) algorithm is proposed by considering three factors: past control inputs, system outputs, and external reference trajectories. Before the algorithm is proposed, a transformation is made to the original system according to the characteristics of the time-delay system, so that the time-delay number can be reduced or become a delay-free system. A novel data-driven state equation is derived from the historical data of the three factors, and then, it is adopted to solve the optimal control of multi-delay systems. Further results show that the proposed DDVI algorithm is convergent and the tracking error is asymptotically stable. Finally, simulations are provided to show the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite-time H ∞ control for discrete-time switched linear systems via admissible edge-dependent switching. The admissible edge-dependent average dwell-time (AED–ADT) is employed to identify a class of constrained switching signals for the resulting closed-loop system. Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and H ∞ performance by incorporating the idea of AED–ADT. By constructing the MDLFs in quadratic forms, a synthesis condition for finite-time bounded control is first proposed, then a synthesis condition for finite-time H ∞ control is further developed based on the obtained result. Finally, two simulation examples are given to verify the effectiveness and practicability of the presented control synthesis method. [ABSTRACT FROM AUTHOR]

In this paper, a new parametric approach is developed for disturbance attenuation in observer design of linear time-invariant systems. First, based on the general solution to a type of generalised Sylvester equations, a complete parametric form of the observer gain matrix is established. Secondly, a new disturbance attenuation index is introduced, and the parameters are further optimised to minimise the index. Under certain conditions, the optimal solution of this optimisation problem is obtained. Finally, the proposed method is used to design the robust observer for the yaw/roll channel attitude control system of a nonrotating missile. It is verified from the simulation results that the proposed method shows a stronger tolerance to disturbances compared with the traditional robust pole assignment method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly focus on the problem of quantised feedback stabilisation of a stochastic discrete-time linear system with white noise input. The dynamic quantiser is used here. The stability of the system under state quantisation and input quantisation is analysed in detail, respectively. Both the convergence of the state's mean and the boundedness of the state's covariance matrix norm should be considered when analysing its stability. It is shown that for the two situations of the state quantisation and the input quantisation, if the system without noise input can be stabilised by a linear feedback law, it must be stabilised by the dynamic quantised feedback control policy. The sufficient conditions that the dynamic quantiser should satisfy are given. Using the results obtained in this paper, one can test whether the stochastic system is stabilisable or not. Numerical examples are given to show the effectiveness of the results. [ABSTRACT FROM PUBLISHER]

This paper considers the dynamic anti-windup design problem for linear systems with time-varying state delay, input saturations and external disturbances. A dynamic anti-windup compensator is first designed that is dependent on the upper bound of the time-varying delay. Then, using an augmented Lyapunov–Krasovskii functional, a distributed-delay-dependent sector condition, some advanced inequalities and some congruence transformations, sufficient conditions are established under which the state trajectories of the closed-loop systems are bounded and meanwhile, the H ∞ performance can be guaranteed. The anti-windup compensator gain can be explicitly solved by means of linear matrix inequalities. For the case of constant delay, the corresponding result is also presented. Finally, two numerical examples illustrate the effectiveness and advantages of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the formation-containment (FC) control issue for heterogeneous linear multi-agent systems (MASs) via distributed event-triggered control. The target for leaders is to form a time-varying formation (TVF) shape around a reference signal which is the virtual leader. To estimate the virtual leader's state, we devise an adaptive event-triggered observer for leaders. In that case, followers are required to converge to the convex combinations of the leaders' outputs. Similarly, another observer is designed for followers to estimate the state information of the convex hull. With the TVF shapes and local sampled information of the designed observers, two distributed event-based protocols are proposed for leaders and followers based on the output regulation framework. Continuous communications are not required for either control laws updating or triggering functions and it is proved that Zeno behaviour is strictly excluded for each agent. Finally, a simulation example is provided to demonstrate the practicability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with adaptive event-triggered consensus of general linear multi-agent systems (MASs). Leaderless consensus and leader-following consensus are both considered. In order to avoid dependence on global information about system topology and reduce communication frequency, distributed adaptive event-triggered consensus protocols are designed. Through model transformation, the consensus problems of MASs are transformed into the stability problems of the corresponding error systems. By using algebraic graph theory and Lyapunov stability theory, some sufficient criteria for MASs to achieve consensus are obtained. Meanwhile, it is proved that the proposed event-trigger conditions can exclude Zeno behaviour effectively. One simulation example is provided to validate the effectiveness of obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the stochastic optimal control of a multi-period mean-variance trade-off performance criterion with and without constraints for discrete-time linear systems subject to multiplicative noises. We adopt a mean-field approach to tackle the problem and obtain a solution for the unconstrained case in terms of a Riccati-like difference equation. From this general result, we obtain a sufficient condition for a closed-form solution for one of the constrained problems considered in the paper. When particularised to the portfolio selection problem, we show that our results retrieve some of the results available in the literature. We conclude the paper by illustrating the obtained optimal controls with a multi-period portfolio selection problem where we minimise the sum of the mean-variance trade-off costs of a portfolio against a benchmark along the time. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on some behaviours of the bounded input-bounded output (BIBO) stability boundary in the linear distributed-order system (LDOS). Finding an association between changes of weight functions of LDOS and variation of its BIBO stability boundary is the other aim of this paper. To achieve these goals, the tangential lines of the BIBO stability boundary for the extremely high and low frequencies are founded in the first step. Then, the additive identity and the multiplicative identity for the weight function maintaining the stability boundary intact are determined. In addition, it is proved that multiplying a set of multiplication factors in the form of polynomials to the weight functions would guarantee the increment of the stability region. To validate the presented results, comparisons among the stability boundary of several different LDOS are performed. Simulation outcomes are in agreement with the extracted results. [ABSTRACT FROM AUTHOR]

In this paper, the set-membership filtering problem is investigated for a class of piecewise linear systems with state constraintsand censored measurements under the Round-Robin (RR) protocol. First of all, the mode of the piecewise linear system is determined by itsstate. The noises under consideration satisfy two ellipsoid constraints. According the schedule of the RR protocol, a set of piecewise linearfilters is constructed in terms of the censored measurements transmitted through the shared network. The objective of this paper is todesign a set of filter gains such that the augmented dynamics satisfies the desirable ellipsoid constraint in the simultaneous presence of stateconstraints, censored measurements and RR protocol. A sufficient condition for the existence of piecewise linear filters is obtained and aconvex optimisation method is presented to derive the minimized ellipsoid in the sense of matrix trace. Finally, a simulation example is givento verify the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to design a high-order repetitive model reference controller (HO-RMRC) for a discrete-time linear system that is subject to uncertain periodic references and disturbances. The controller design method we propose is established by combining two controller design schemes: high-order repetitive control (HORC) and model reference control (MRC). Here, the HORC is used to suppress uncertain periodic disturbances significantly and the MRC is used to track time-varying references without introducing new transient responses. The stability analysis of the resulting closed-loop system is provided and describes how admissible learning gains are determined to achieve stability and a desirable convergence rate. The efficacy of the proposed control method is demonstrated via numerical simulations where the performance of the resulting HO-RMRC is compared with those of the HORC and the MRC as standalone controllers. It is evident that the HO-RMRC outperforms the HORC and the MRC in simultaneously achieving perfect reference tracking and disturbance cancellation/attenuation. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing distributed state estimation solutions for a network of interconnected systems modelled by linear time-varying (LTV) dynamics in a discrete-time framework. The problem is formulated as a classical optimal estimation problem, for the global system, subject to a given sparsity constraint on the filter gain, which reflects the distributed nature of the network. Two methods are presented, both of them able to compute a sequence of well-performing stabilising gains. Moreover, both methods are validated by resorting to simulations of: (i) a randomly generated synthetic LTV system; and (ii) a large-scale nonlinear network of interconnected tanks. One of the proposed methods relies on a computationally efficient solution, thus it is computed very rapidly. The other achieves better performance, but it is computationally more expensive and requires that a window of the future dynamics of the system is known. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well-performing gains that stabilise the estimation error dynamics. Both algorithms are scalable, being adequate for implementation in large-scale networks. [ABSTRACT FROM AUTHOR]

This paper first investigates robust tracking problem of a high-order iterative learning control (HOILC) algorithm for two classes of two-dimensional linear discrete time-varying Fornasini–Marchesini systems (2-D LDTVFMS) and 2-D LDTVFMS with input delays with iteration-dependent reference trajectory described by a high-order internal model (HOIM) operator, boundary states and disturbances. An extended high-order linear discrete inequality is proposed to guarantee the ILC tracking error of 2-D LDTVFMS converge robustly to a bounded range, the bound of which is relied on iteration-dependent uncertainties from reference trajectory, boundary states and disturbances. A simulation example on a practical thermal process is used to validate the effectiveness and feasibility of the proposed HOILC law. Additionally, it is verified by theory analysis and simulation that no matter how the ILC controller gain is selected, the convergence condition in Theorem 2 of Wan and Li [(2021). High-order internal model based iterative learning control for 2-D linear FMMI systems with iteration-varying trajectory tracking. IEEE Transactions on Systems Man and Cybernetics: Systems, 51, 1462–1472] is not satisfied. Using the proposed HOILC law, perfect tracking result in Theorem 2 of Wan and Li (2021) can be obtained. [ABSTRACT FROM AUTHOR]

Predictor feedback controllers are irreplaceable and widely used for systems with long input delays. However, it is also known to be sensitive to mismatch between the nominal input delay and the true unknown one. In this paper, we propose a robust predictor feedback controller design to enlarge the admissible delay mismatch, while keeping the convergence rate within a prescribed level. It is shown that the controller synthesis problem can be cast into a generalised eigenvalue problem (GEVP). [ABSTRACT FROM AUTHOR]

A basic introduction to high-order fully actuated (HOFA) approaches for discrete-time systems is given. Firstly, it is shown that, different from the continuous-time systems, general dynamical discrete-time systems can be represented by two types of discrete-time HOFA models, namely, the step forward HOFA models and the step backward HOFA models. Secondly, controllers for the step backward HOFA models are designed, which result in constant linear closed-loop systems with arbitrarily assignable eigenstructures. The related problem of feasibility is also discussed. The well-known discrete-time feedback linearisable systems and strict-feedback systems are shown to be equivalent to both the step forward and step backward HOFA models. Finally, a generalised step backward HOFA model containing control vectors of different time instants is proposed and investigated and demonstrated with a type of proposed pseudo feed-forward systems. The contribution in this paper has laid a fundamental basis for discrete-time HOFA approaches. Further analysis and design problems can be naturally established parallel to the continuous-time system case. [ABSTRACT FROM AUTHOR]

The principal drawback of traditional adaptive systems is the possibility of rather poor transient response. In this regard, the multiple-model methodology has been beneficial over the past couple of decades. However, the application of this methodology requires proven indirect model reference adaptive control. Such a gap exists in the case of discrete-time linear time-invariant systems with unknown parameters. The principal contribution of this paper is to fill this void by arriving at proof of global stability of discrete-time adaptive systems that use the prediction error rather than the control error to update the parameters of the prediction model. This proof is based on the theory of Lyapunov and the properties of square-summable sequences. An analysis of the available literature reveals that such a result is not available even for linear time-invariant systems. Therefore, the proof is first provided for adaptive systems with a single prediction model wherein the transfer function of the plant has an arbitrary relative degree. Subsequently, this proof is extended to the case of multiple prediction models in the context of multiple-model methodology with second-level adaptation. Two parameter update algorithms are considered. Simulation studies are included to demonstrate the improvement in transient performance. [ABSTRACT FROM AUTHOR]

In this paper, the classical optimal control problem in air transportation system is studied. The optimisation model is based on the principle of 'first come first serve' and the arrival traffic flow only occurs in the first queue which is assumed to be infinite. In addition, it is assumed that all processing times and arrival intervals are predefined. This paper aims to propose a new optimal control problem of series air traffic system and an effective solution. The exact algorithm of each sub-segment is given, and the required results are obtained. Numerical experiments show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a new problem of static output feedback controllers design for positive systems with delayed output measurements. When delayed output measurements are exclusively used as feedback control signals, previous control design methods for positive systems relying on the so-called delay-independent positivity and stability conditions are unable to synthesise a stable static output feedback controller for positive systems. A new method based on delay-dependent positivity and stability conditions is proposed in this paper to tackle this issue. We show that the synthesis of static output feedback controllers for positive systems under the effect of delayed output measurements is feasible under the newly proposed design method. Numerical examples are given to demonstrate the effectiveness of the new result. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of distributedly estimate the state of a plant through a network of interconnected agents. Each of these agents must perform a real-time monitoring of the plant state, counting on the measurements of local plant outputs and on the exchange of information with neighbouring agents. The paper introduces a distributed LQ-based design that is applied to a distributed observer structure based on a multi-hop subspace decomposition. Stability and optimality conditions are derived and tested in simulation. Finally, the design method presented allows the user, through the tune of two scalar parameters, to modify the observer gains according to their experience about the plant. [ABSTRACT FROM AUTHOR]

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the parametric generalised Sylvester matrix equation , whose elements are linear functions of uncertain parameters varying within intervals. This model generalises both interval matrix equations and parametric interval linear systems, so it is a quite general model. First, we give some sufficient conditions under which the solution set of this parametric equation is bounded. We then propose several approaches for enclosing the solution set that acquire tighter enclosures than those obtained by relaxing the parametric system to an interval system. Some special cases of interval systems that inherently are parametric (have dependent structure) are considered, too. Finally, numerical experiments are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes new conditions for the design of a robust partial sampled-data state feedback control law for Markov jump linear systems (MJLS). Although, as usual, the control structure depends on the Markov mode, only the state variable is sampled in order to cope with a specific network control structure. For analysis, an equivalent hybrid system is proposed and a two-point boundary value problem (TPBVP) that ensures minimum or cost is defined. For control synthesis, it is rewritten as a convex set of sufficient conditions leading to minimum guaranteed cost of the mentioned performance classes. The optimality conditions are expressed through differential linear matrix inequalities (DLMIs), a useful mathematical device that can be handled by means of any available LMI solver. Examples are included for illustration. [ABSTRACT FROM AUTHOR]

To save resource of communication, this paper investigates the model-based event-triggered control systems. Two main problems are considered in this paper. One is, for given plant and model, to design event conditions to guarantee the stability of the systems. The other is to consider the effect of the model matrices on the stability. The results show that the closed-loop systems can be asymptotically stabilised with any model matrices in compact sets if the parameters in the event conditions are within the designed ranges. Then, a separation property of model-based event-triggered control is proposed. Namely, the design of the controller gain and the event condition can be separated from the selection of the model matrices. Based on this property, an adaption mechanism is introduced to the model-based event-triggered control systems, which can further improve the sampling performance. Finally, a numerical example is given to show the efficiency and feasibility of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, the stability analysis of linear systems with an interval time-varying delay is investigated. First, augmented Lyapunov–Krasovskii functionals are constructed, which include more information of the delay's range and the delay's derivative. Second, two improved integral inequalities, which are less conservative than Jensen's integral inequalities, and delay-range-partition approach are utilised to estimate the upper bounds of the derivatives of the augmented Lyapunov–Krasovskii functionals. Then, less conservative stability criteria are proposed no matter whether the lower bound of delay is zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numerical examples are given and their results are compared with the existing results. [ABSTRACT FROM PUBLISHER]