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This paper solves the problem of designing positive functional $ H_{\infty } $ H ∞ filters for positive linear time-delay systems. In fact, we propose a new positive reduced order $ H_{\infty } $ H ∞ filter for positive linear constant state time-delay systems for which the states remain in the nonnegative orthant of the state space, subject to disturbances and unknown inputs. This paper is a first attempt to design positive unknown inputs functional $ H_{\infty } $ H ∞ filter for such positive linear delayed systems. The proposed approach is based on the positivity of an augmented system composed of dynamics of both considered system and proposed filter, on the unbiasedness of the estimation error by the resolution of Sylvester equation and also on Lyapunov-Krasovskii stability theory; then conditions for the establishment of such filters are formulated in terms of an optimization problem. An algorithm that summarizes the different steps of the proposed positive functional $ H_{\infty } $ H ∞ filter design is given. Finally, numerical example and simulation results are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

'Co-design' problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS). [ABSTRACT FROM AUTHOR]

The Lyapunov approach is one of the most effective and efficient means of studying the partial stability of stochastic systems. A number of authors have analysed the partial practical stability of stochastic differential equations using Lyapunov techniques. Nevertheless, no results are concerned with the partial stability of stochastic systems based on the knowledge of the solution of the system explicitly. This paper has been concerned with the problem of partial practical stability for linear time-varying stochastic perturbed systems. Necessary and sufficient conditions for partial practical uniform exponential stability are given based on generalised Gronwall inequalities, in particular of Gamidov's type. An example is developed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This paper develops a methodology for designing a control system composed of a linear time-invariant system interconnecting with multiple decoupled time-invariant memoryless nonlinearities. The design problem is to determine parameters of the system such that its outputs and the nonlinearity inputs always remain within prescribed bounds for all exogenous inputs whose magnitude and slope satisfy certain bounding conditions. By using Schauder fixed point theorem, we show that a design associated with a linear system is also a solution of the problem. Based on this, we further develop surrogate design criteria in the form of the inequalities that can readily be solved in practice. Sufficient conditions for the solvability of such inequalities are given for deadzone and saturation. To show the usefulness and the effectiveness of the methodology, a design example of a load frequency control system with time delay is carried out where deadzone and saturation are taken into account. [ABSTRACT FROM AUTHOR]

This paper presents a numerical approach to solve the estimator-based filtering problem of a linear system with multiple and distributed delays. We consider the problem of finding a filter or estimator that suppresses the $ \mathcal {H}_2 $ H 2 filtering cost on the transfer matrix from a given noise input to the filtering error. By solving an optimisation problem associated with the $ \mathcal {H}_2 $ H 2 performance, the gain matrices of the filter are obtained. The effectiveness of the presented approach is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the converse problems about the robust stability of finite dimensional negative imaginary systems. Various converse negative imaginary theorems are established for linear time-invariant systems. It is shown that the feedback interconnection stability of a specific system with an arbitrary strictly negative imaginary system implies the negative imaginary property of the specific. [ABSTRACT FROM AUTHOR]

In networked control systems, the communication load is a main concern for implementing model predictive control (MPC). This paper introduces a self-triggered MPC algorithm under network environments to reduce communication load, for discrete-time linear systems with bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly based on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered model predictive control of a nominal system. Moreover, the new cost function explicitly adopts communication load is in consideration. The proposed algorithm is proved to drive the system to an invariant set with respect to the bounded disturbances. Finally, simulation results is provided to verify the effectiveness of the proposed robust output feedback MPC algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel data-driven invariant-based safe control scheme for control of a nonlinear vehicle is developed. First, a novel incremental finite-time Koopman representation-based identifier is introduced to learn approximated lifted-states linear system model of system from a limited budget of incrementally sampled data points which not only minimises the instantaneous Koopman representation's identification errors but also the identification errors for a batch of past samples collected in a history stack. A great advantage of the presented identifier is that the uncertainty of the identified system is also quantified and updated over time on a slower time scale. Using set-theoretic tools, then, the quantified uncertainty will be leveraged in conjunction with the learned model in order to impose robust contractivity on the safe set, which guarantees its safety and stability. The proposed approach significantly reduces conservativeness through quantifying and updating the uncertainty level of the learned model over time. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problems of existence and computation of proper and stable stabilising compensators in the feedback path of a special class of linear time-invariant multivariable systems characterised by a strictly proper transfer function matrix. For the class of systems that are 'square', i.e. have the same number of inputs and outputs and have no zeros in the closed right half complex plane and the class of 'non-square' systems that include a 'square' subsystem that has no zeros in the closed right half complex plane we present a sufficient condition for the existence and computation of proper stabilising (pole placing) compensators which in certain cases that depend on the transfer function matrix of the system can be chosen to be stable. [ABSTRACT FROM AUTHOR]

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory. [ABSTRACT FROM AUTHOR]

The focus of this paper is the design of open-loop control profiles for linear differentially flat systems whose model parameters are uncertain and are represented probabilistically. To account for the time-invariant model parameter uncertainties, polynomial chaos is used to derive a surrogate model which permits easy evaluation of the mean and variance of the uncertain states. A chance constrained optimisation problem is posed to minimise the terminal error of the stochastic states for a prescribed risk of not satisfying the terminal state bounds. To permit posing a convex optimisation problem, the cost function which is the residual energy is approximated by a hypercube circumscribing the hypersphere which bounds the terminal residual error. This relaxation permits posing a convex optimisation problem to arrive at the robust control profile. The proposed technique is illustrated on two examples including the benchmark spring-mass-dashpot system undergoing a rest-to-rest maneuver and a UAV undergoing a translation in a prescribed time. Parametric studies are conducted where the impact of varying the order of the polynomial chaos expansion and the degree of the parameterised control profiles are used to conclude that a 2–3 degree polynomial chaos expansion is sufficient to capture the time evolution of the mean and variance of the states which are required for the chance constrained optimisation problems. As expected, the design results in improved performance as the number of free variables used to parameterise the control profiles increases. [ABSTRACT FROM AUTHOR]

In this paper we present and provide a proof for a set of non-recursive formulae arising in the computation of the largest output-nulling and the smallest input-containing subspaces which have been used in a variety of contexts in the framework of the geometric approach. These expressions have been used in the literature both in the strictly proper and in the non-strictly proper case, but, to the best of our knowledge, a proof is still missing. These formulae are established here in the general possibly non-strictly proper case. Some ancillary side results of independent interest are also proposed. [ABSTRACT FROM AUTHOR]

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance. [ABSTRACT FROM AUTHOR]

This paper considers model order reduction based on low-rank decomposition of the cross Gramian for linear systems. The proposed approach uses the low-rank factors of the cross Gramian to generate approximate balanced model for the large-scale system. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate Hankel singular values. The low-rank factors are directly constructed from the expansion coefficients of impulse responses in the space spanned by Legendre polynomials by solving block tridiagonal linear systems. In contrast to balanced truncation related approaches which require to solve Sylvester equation to compute the full cross Gramian, the proposed method needs to solve sparse linear equations, and only one singular value decomposition is applied to a low-dimensional matrix. The stability preservation of the reduced model is briefly discussed. And in combination with the dominant subspace projection method, the reduction procedure is modified to alleviate the shortcoming, which may unexpectedly lead to unstable systems even though the original one is stable. Finally, numerical experiments are given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, by extending the controllability and Brunovsky indices for a matrix pair to a matrix quadruple, three kinds of indices, say, the invertibility indices, the left invertibility indices, and the right invertibility indices, for linear time-invariant systems are introduced and studied. Based on properties of these indices, a neat expression for the Morse lists of a linear system is given without transforming it into its Morse normal form, which is a deep and fundamental result in linear systems theory, and takes an important role in many analysis and design problems for linear systems. Furthermore, the Morse normal form with only algebraic equivalence transformation is also investigated and is simplified. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time boundedness (FTB) of linear time-invariant systems that are affected by a disturbance generated by an exosystem. By using a time-invariant quadratic Lyapunov function, Finsler's lemma and a dual system approach, new sufficient linear matrix inequalities (LMIs) conditions are given for analysis and synthesis for FTB. These results are extended: first, to finite-time stability (FTS) of linear time-invariant systems, second, to their input–output FTS associated, or not, to FTB. All the conditions are given in terms of LMIs, which make them easily tractable. Finally, the computational efficiency and the conservatism reduction of our approach are illustrated through an illustrative example. [ABSTRACT FROM AUTHOR]

This paper develops a distributed consensus control protocol that guarantees consensus tracking and global optimality with respect to a positive quadratic performance index for identical general linear multi-agent systems on an undirected graph. By using the previewable future reference signal, the consensus tracking control problem is converted into a preview control based optimal problem. The inverse optimality theory is introduced to overcome the difficulty of designing a distributed optimal controller, which is caused by the fact that the communication topology always interplays with the system dynamics and subsequently the global information is usually required in a conventional optimal controller design. First, a distributed optimal controller for tracking a reference signal with stable mode is designed. Then, an internal model based distributed optimal controller is further designed to track a time-varying reference signal. The structured quadratic performance indexes are derived for both cases, respectively, and based on which, two distributed optimal tracking control protocols are implemented to guarantee the asymptotic stability of the augmented systems only using local information. Simulation results show that an appropriate preview length can effectively improve the tracking performance. [ABSTRACT FROM AUTHOR]

This paper addresses the state-dependent switching design problem for impulsive switched linear systems under dwell-time constraints. All conditions are presented as optimisation problems that are convex for some fixed set of scalars. Applications to sampled-data systems are presented and illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time annular domain stability and stabilisation for the positive systems. A new analysis method is proposed to obtain less conservative finite-time annular domain stability criteria and its superiority to modified Gronwall inequality is analysed. Moreover, conditions for the existence of state feedback and observer-based controllers that guarantee the closed-loop system to be positive and finite-time annular domain stable are given under the linear programming framework. Finally, two numerical examples are provided to show the effectiveness and superiority of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents the H 2 State-Feedback Control for Continuous Semi-Markov Jump Linear Systems where the transition rates are given by the ratio of polynomials of the sojourn time. We show that, for instance, Rayleigh-, Erlang- and a class of Weibull-distributed sojourn time can be described by such a model. We present general results on the stability and on the H 2 of Semi-Markov Jump Linear Systems and provide sum-of-squares conditions for norm calculation and state-feedback control design problems. We conclude the paper by presenting two numerical examples that point out the main features of our results and by discussing future directions and related problems. [ABSTRACT FROM AUTHOR]

This paper presents the stability and performance conditions for discrete-time constrained switched linear systems under arbitrary switching. Design methods for such systems, which constrain the set of admissible switching sequences to attain stability and a desired performance level, are also presented. The key procedures presented in this paper are based on classic convex optimisation and graph theory results. Simulations and numerical examples are included to illustrate the main features of the developed theory. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some finite-time control problems for stochastic linear time-varying systems, described by an Itô type differential equation. In particular, the annular stochastic finite-time stability control problem is dealt with. In this context, it is required that the norm of the state variables remains bounded between an inner and an outer ellipsoid, during a finite-interval of time. The first contribution of the paper consists of two sufficient conditions for stability, which are derived by exploiting an approach based on time-varying quadratic Lyapunov functions. The first condition requires the solution of two generalised differential Lyapunov equations; the latter the existence of a feasible solution to a pair of differential linear matrix inequalities. As particular cases, we obtain sufficient conditions for stochastic finite-time stability (in this last case, the lower ellipsoid collapses to the origin). From the analysis conditions, a sufficient condition is derived for the annular stochastic finite-time stabilisation via both state and output feedback. Some numerical examples illustrate the application of the proposed methodology and show that our approach attains less conservative results than those obtainable with the existing literature. Moreover, an application of the annular stochastic finite-time stability approach to the stabilisation problem of a satellite with respect to the geomagnetic field is presented. [ABSTRACT FROM AUTHOR]

This paper is devoted to the guaranteed cost H ∞ of continuous-time linear parameter-varying (LPV) systems, considering the gain scheduling (GS) strategy and the state derivative feedback (SDF). The main contribution of the paper is to derive linear matrix inequalities (LMIs) conditions for the H ∞ -SDF problem for LPV systems, taking into account the GS controller. For the good behaviour of the controller, we assume that the time-varying parameters are available for online measurement. In some cases, the H ∞ -GS-SDF controller obtained high control signals, and as we intend to apply the proposed method in practical situations, we introduce the concept of D -stability in the problem approach. Examples and a practical implementation 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 guaranteed cost H ∞ minimisation. [ABSTRACT FROM AUTHOR]

The paper analyses a networked control system consisting of a linear time-invariant system with a static feedback nonlinearity, subject to large delays in the feedback loop. This model is valid for example in wireless data flow control, where a saturation occurs since the flow is one-directional. The present paper extends previous results by proving necessity, in case the loop gain is uniformly less than one. The results are validated and illustrated in a simulation study. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of almost sure ultimate bound estimation and controller design for Markov jump linear systems with bounded stochastic disturbances. By utilising a Lyapunov-based scheme proposed in this paper, an almost sure estimation of ellipsoidal ultimate bound (EUB) of the system is obtained through tractable matrix inequalities. On the basis of the estimation results, the problem of designing mode-dependent state feedback controllers that make the closed-loop system admit a prescribed ellipsoid as an EUB is considered. The obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information. Finally, a practical example in DC motor devices is presented to demonstrate the applicability of the obtained results. [ABSTRACT FROM AUTHOR]

This paper presents a bicoprime factorisation approach to deal with various stability problems for linear discrete time-varying systems within the framework of nest algebra. First, we show that a system has a bicoprime factorisation if and only if it has a right and left coprime factorisation by using the complete finiteness of the nest algebra. Based on the bicoprime factorisations, some stability criteria for internal stability and strong stabilisability are obtained, which generalises similar results for linear time-invariant systems. Finally, we derive a necessary and sufficient condition for simultaneous stabilisability of two systems, Additionally, the condition given in this paper lead to a constructive controller design to stabilise simultaneously two systems. [ABSTRACT FROM AUTHOR]

In this paper, the set-membership state and parameter estimation problems are considered for linear time-varying systems. The noises in the system are unknown but bounded and the variation of parameters is considered as a bounded expansion. The entire estimator is an interactive estimation of parameters and states. In parameter estimation, the exact set of parameter estimates may be non-convex because of the uncertain states. A polytopic linear parameter varying (LPV) enclosure of the system regression expression is constructed as a convex relaxation. The result of parameter estimation is a set to include the true parameter of the model. Meanwhile, in the state estimation, a similar LPV enclosure of the state-space model is also used to bound the state matrix uncertainties. This LPV enclosure in the state estimation is narrowed by the parameter estimation, and then the set of state estimates is computed to include the true state. The constrained zonotope (CZ) is used to describe sets of interest and the necessary set operations are expanded to LPV mapping. Because of the highly adjustable accuracy of CZ, the proposed algorithm can make a better trade-off between computational accuracy and efficiency. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we prove that stabilisability is a static output feedback (SOF) invariant, for scalar and multivariable systems. Then we examine scalar stabilisability, from an invariant viewpoint. We prove that the signature of Hermite's Bezoutian is constant within certain intervals that we call critical, and we give a very simple algebraic stabilisability criterion, consisted of a finite number of stability checks, one for each critical interval. We establish the validity of this criterion with Routh, Hurwitz and Lyapunov methods. We prove that the winding number of the Nyquist plot around points of the real axis, is constant within critical intervals. We correlate the stabilisability within critical intervals with the stability of corresponding critical polynomials defined at their limits. Finally, we discuss why our findings constitute a decisive step towards the analytical solution for the persisting problem of static output feedback stabilizability of linear time invariant multivariable systems. [ABSTRACT FROM AUTHOR]

This paper describes a solution to the problem of fault-tolerant control (FTC) problem for leader-following heterogeneous linear multi-agent systems (MASs) subject to loss of effectiveness and time-varying additive actuator faults. The main goal of the proposed FTC approach is to maintain the behaviour of the heterogeneous MASs in spite of actuator faults and to save on bandwidth required for the MASs communication by using a dynamic event-triggered communication mechanism. Firstly, a fault estimation observer, which deals with linear systems with matched disturbances, is constructed to estimate simultaneously the actuator faults and the followers' states. Then, an FTC with dynamic event-triggered communication is proposed. The latter is based on a dynamic internal reference for each agent and exploits the estimated faults. Thus, it is at first shown that the FTC problem can be indirectly solved through the consensus tracking of the defined internal references. Then, a sufficient condition of consensus tracking for the internal references with a dynamic event-triggered communication is proposed. Finally, a sufficient and necessary condition is derived for the FTC of linear heterogeneous multi-agent systems. The effectiveness of the proposed approach is illustrated with a numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, the networked model predictive control (MPC) for the linear system with the arbitrary bounded delays and packet losses during the data transmission and processing is studied. Since MPC requires the prediction of the input and state within the two links (i.e. sensor to controller and controller to actuator links), the closed-loop model is constructed by considering all possible transmission statuses. The obtained controller generalises the results of Kothare et al. (1996), in specifying the system model, physical constraints and closed-loop stability, while guaranteeing the recursive feasibility of the optimisation problem. Two simulations are implemented to show the effectiveness of the presented networked MPC approach. [ABSTRACT FROM AUTHOR]

This paper considers the prescribed-time stabilisation of the linear system with matched unknown external disturbance. The disturbance is supposed to be generated by an exogenous system. In the case only the~output signal of the original system is available for feedback, a prescribed-time linear observer for the augmented system consisting of the original system and the exogenous system is designed. Then the prescribed-time stabilisation problem can be achieved by using the state-and-disturbance-observer-based periodic delay feedback. Furthermore, in the case the state of the original system is measurable, three classes of prescribed-time disturbance observers for the exogenous system are designed. The prescribed-time stabilisation problem can also be solved by applying the disturbance-observer-based periodic delay feedback. A numerical example is posted to demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, the sparse feedback stabilisation in which the gain matrix has as many zero components as possible in linear delay systems is investigated. The necessary and sufficient condition for the asymptotic stability of the delay systems under sparse state feedback is given. By means of a special matrix norm and the transition matrix (fundamental matrix) of delay systems, the sparse gain matrix design problem is transformed into an optimisation problem. We further derive the proximal mapping of the special matrix norm, and then based on the gradient descent of the smooth part of the objective function, the proximal gradient method is introduced to develop an algorithm for solving the non-smooth optimisation problem. Numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a reduced-order interval observer (R-IO) design technique is developed for continuous-time descriptor linear-parameter-varying systems with unknown-but-bounded uncertainties. First, by introducing an intermediate variable, the R-IO design amounts to estimating the linear functional of the system states. Then, with a parameter-dependent Luenberger-like structure, the R-IO existence condition is eventually formulated into a set of differential-algebraic equations, not involving any linear transformation process. Further, a parametric solution to such an R-IO is derived through solving the equation set, which clearly shows the design degrees of freedom. Finally, the correctness of the proposed results is verified by a numerical system and an electrical circuit system. [ABSTRACT FROM AUTHOR]

In this paper, the stability issue for a class of cyclic switched linear systems with all stable or partly unstable submodes is investigated. Firstly, the new concepts of stable cyclic sequence-dependent cycle dwell time (S-CDT) and unstable cyclic sequence-dependent cycle dwell time (U-CDT) are proposed for the first time. Then, based on linear matrix inequalities (multiple Lyapunov functions) and cycle dwell time (CDT) switching law, the stability conditions for slowly cyclic switched linear (nonlinear) systems with all stable submodes are established. Furthermore, by using linear matrix inequalities (multiple Lyapunov functions), S-CDT and U-CDT switching laws, the stability criteria are derived for slowly and fastly cyclic switched linear (nonlinear) systems with a designed cyclic switching scheme where slow S-CDT switching and fast U-CDT switching are, respectively, applied to partly stable and partly unstable submodes. Finally, three numerical examples are presented to demonstrate the feasibility of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the structural controllability problems of a class of driftless discrete-time bilinear systems which have nearly the same structure as linear systems. Algebraic as well as graph-theoretic conditions for structural controllability of such systems with single-input and multi-input are, respectively, obtained. Furthermore, we introduce a new notion, called structural near controllability, for those structured systems which cannot be structurally controllable but structurally nearly-controllable. It is shown that the bilinear systems can be structurally nearly-controllable although their linear counterparts can never have a large controllable region no matter what the parameters are chosen. Necessary and sufficient conditions for structural near-controllability of the bilinear systems are thus derived. We also consider the structural controllability problem in the continuous-time case. Examples and graphs are given to illustrate the obtained results of this paper. [ABSTRACT FROM AUTHOR]

This paper deals with finite-time stability, boundedness and stabilisation of discrete-time linear systems with regards to polyhedral domains. The key observation made in this paper is that finite-time stability properties can be analysed in terms of reachable sets. We first establish necessary and sufficient conditions for finite-time stability and boundedness of nominal systems, expressible as linear programming problems. We then present sufficient conditions that may be used to compute feedback control to render such systems finite-time stable/bounded. Finally we generalise the above results to the case of discrete-time linear systems with polytopic uncertainty subject to a bounded disturbance. [ABSTRACT FROM AUTHOR]

This paper addresses novel H 2 and L 2 norm-based controller designs for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). Despite the importance of LPV/LFR systems to the control literature, there is a lack of works on this topic. The distinctive formulation of the proposed controller designs is given by using parameter-dependent Lyapunov functions in combination with slack variables and general full-block multipliers. Such proposed formulation leads to less conservative synthesis conditions characterised in terms of a finite number of linear matrix inequalities for both state-feedback and static output-feedback controllers subject to H 2 and L 2 performances for discrete-time LPV/LFR systems. Improvements obtained by the proposed controller design conditions over existing methods in the area are assessed by numerical examples. [ABSTRACT FROM AUTHOR]

This paper concentrates on the stability analysis of continuous-time linear systems with multiple time-varying delays. The time-delays are assumed to be bounded and have or not lower and upper bounds on their time-derivative. Based on the Lyapunov-Krasovskii theory the proposed results formulated as linear matrix inequality conditions can verify the delay-intervals for which the system stability is preserved. The main results follow from developing new augmented Lyapunov-Krasovskii functionals that exploit the benefits of the Bessel-Legendre-based integral inequality and the reciprocally convex approach. Also, the proposed functionals allow us to take advantage of the relationships between the current and delayed states. As a result, the proposed stability conditions outperformed similar existing ones in all numerical tests accomplished in this paper. [ABSTRACT FROM AUTHOR]

In this work, we consider the problem of simultaneously estimating the system states and unknown inputs in a linear sampled-data system, whose dynamics is influenced by external disturbances and uncertainties. Hardware limitations prevent an estimation scheme for a sampled-data system from achieving finite-time convergence, which is a typical property of existing sliding mode observers for dynamical continuous-time systems, because the sampling period is finite. Due to the sampling process, an approximate implementation of such an observer, designed for a continuous-time system, may not retain the desired performance in the sampled-data context. In this paper, we present an observer which takes advantage of the quasi-sliding motion concept to simultaneously estimate the state variables and the unknown input signals in a sampled-data context. A theoretical study is conducted to formally justify the convergence properties of the observer whilst simulation results are provided to show the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we study the connections between two classical notions of equivalence used in the literature of linear multidimensional (nD) systems. On one hand, we have the notion of zero coprime system equivalence which has been proved to be well suited for the preservation of input–output properties. On the other hand, we have the notion of equivalence induced by the algebraic analysis approach to linear systems theory which preserves algebraic properties of the associated module. We first prove that a zero coprime system equivalence yields an equivalence in the sense of algebraic analysis. Conversely, we show that, under some conditions, an equivalence in the sense of algebraic analysis provides a zero coprime system equivalence. In both cases, the results are completely explicit. [ABSTRACT FROM AUTHOR]

This paper presents a strategy to compute a suboptimal solution to the finite-horizon linear-quadratic control problem for Markov jump linear parameter-varying systems. The system parameters depend not only on a Markov chain but also on linear parameter-varying elements that take values in convex polytopic sets. The suboptimal approach represents an attempt towards solving the optimal control problem that remains unsolved in the literature. Illustrating that such a suboptimal approach can be of interest when solving practical control problems. Experimental results on the control of an automotive throttle valve subject to failures driven by a Markov chain are discussed, thus supporting the usefulness of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, passivity is used to investigate the formation control problem for second-order multi-agent systems (MASs) with linear or nonlinear coupling. Firstly, the passivity of a single agent is studied by selecting appropriate adaptive state feedback controllers. Moreover, in order to ensure that MASs with nonlinear intrinsic dynamics and linear/nonlinear coupling can converge to a predefined formation, some appropriate control schemes are designed based on the passivity of a single agent. In addition, the passivity-based formation problem for the MASs with double-integrator dynamics is also studied. Finally, the effectiveness of the proposed formation control strategies is demonstrated through two numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a safe model-based reinforcement learning (MBRL) approach to control nonlinear systems described by linear parameter-varying (LPV) models. A variational Bayesian inference Neural Network (BNN) approach is first employed to learn a state-space model with uncertainty quantification from input-output data collected from the system; the model is then utilised for training MBRL to learn control actions for the system with safety guarantees. Specifically, MBRL employs the BNN model to generate simulation environments for training, which avoids safety violations in the exploration stage. To adapt to dynamically varying environments, knowledge on the evolution of LPV model scheduling variables is incorporated in simulation to reduce the discrepancy between the transition distributions of simulation and real environments. Experiments on a parameter-varying double integrator system and a control moment gyroscope (CMG) simulation model demonstrate that the proposed approach can safely achieve desired control performance. [ABSTRACT FROM AUTHOR]

This article studies a new class of nonautonomous second-order nonlocal measure driven control systems involving state-dependent delay (SDD). The system presented in this paper can deal with a large class of hybrid systems with their Zeno behaviour having no restrictions. We use the theory of measure of noncompactness to develop our main results. The existence of a solution to the considered problem is obtained via the Mönch fixed point theorem. The approximate controllability of the aforementioned system is investigated under the assumption that the associated linear system is approximately controllable. To investigate our main results, the integral is taken in the Bochner–Stieltjes sense that makes the obtained results more general. In the end, an example is formulated for the practical usefulness of the established theory. [ABSTRACT FROM AUTHOR]

The contribution of this paper is a control synthesis and stability verification framework for linear time-invariant multiagent systems with heterogeneous actuator dynamics and system uncertainties. In particular, we first propose a distributed adaptive control architecture in a leader-follower setting for this class of high-order multiagent systems. The proposed architecture uses a hedging method, which alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of heterogeneous actuator dynamics of these agents. We then use Lyapunov stability theory and linear matrix inequalities to analyse the proposed architecture. This analysis reveals a stability condition, where evaluation of this condition with respect to a given graph topology allows stability verification of the controlled multiagent system. From a practical point of view, this condition also shows a fundamental tradeoff between heterogeneous agent actuation capabilities and unknown parameters in agent dynamics. Several illustrative numerical examples are also provided to demonstrate the efficacy of the proposed architecture. [ABSTRACT FROM AUTHOR]

This paper studies stability and stabilisation issues of switched linear time-invariant systems with stable/unstable multiple equilibria. Investigation of such switched systems is motivated by a switching economic system. The well-known common Lyapunov function method is shown to be ineffecctive in analysing region stability of switched systems with multiple equilibria via a counterexample. When every subsystem has an equilibrium point and all multiple equilibria pairwise differ, this paper proposes some sufficient conditons for region stability/instability of such switched systems with respect to a region containing all multiple equilibria under arbitrary quasi-periodical switchings. These novel results imply that there may exist stable limit cycles of such switched systems. Based on the stability results, a global asymptotic region-stabilising controller, quasi-periodical switching path, and corresponding algorithm are all designed for such switched control systems. Several illustrative examples demonstrate the effectiveness and practicality of our new results. [ABSTRACT FROM AUTHOR]

Existing adaptive control algorithms at best guarantee that the tracking error is a l2 sequence. This paper presents globally stable adaptive control algorithms for linear discrete-time systems providing l1 tracking performance. Two algorithms with different degree of complexity are proposed, one for the case of known control directions, and a separate algorithm for the case of unknown control directions. It is demonstrated that in both cases the tracking error is l1 sequence, while the input and output signals are uniformly bounded. [ABSTRACT FROM AUTHOR]

The main objective of this paper is the characterisation of the notion of uniform algebraic observability for multi-switching linear systems. In particular, it is shown that a multi-switching linear system is 'generically' uniformly algebraically observable if and only if the number of available measurements is greater than the number of switching signals acting on the systems. This result is established without requiring any knowledge about the (possibly, stochastic) process generating the switching pattern. Moreover, since such systems can be used to model sensor networks, the results given in this paper can 'generically' be used to design simple observers for sensor networks able to cope with sensor failures and data losses. [ABSTRACT FROM AUTHOR]

This paper presents the design of robust hierarchical control for homogeneous linear multi-agent systems (MAS) subject to parametric uncertainty and external disturbance. Specifically, the control design is based on a two-layer hierarchical structure consisting of an upper layer and a lower layer. In the lower layer, each agent is represented by a linear time-invariant system and executes a local action. Moreover, each agent exchanges information with neighbouring agents in the upper layer through an undirected graph to achieve the global goal of stabilisation and disturbance attenuation for the MAS. We propose two robust control designs, namely, robust H ∞ hierarchical control and robust H 2 hierarchical control. The design of local and global feedback control laws is formulated as a constrained optimisation over linear matrix inequalities (LMI). The LMI formulation can effectively incorporate the design objective to minimise disturbance attenuation. Numerical results show that the proposed robust controls ensure robust stability of MAS and outperform the existing nominal controls by improving the disturbance attenuation. [ABSTRACT FROM AUTHOR]