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This paper proposes a novel control structure to solve the infinite-time linear quadratic tracking (LQT) problem. The major challenge in the LQT problem is the boundedness issue of the cost function in an infinite time framework. In many studies, a discount factor is utilised to overcome the challenge. However, it can affect the stability of the closed-loop system and the steady-state error. This paper proposes an optimal control structure that guarantees zero steady-state error with bounded cost function without utilising the discount factor. The optimal gains of the proposed control structure are computed via model-based and model-free reinforcement learning (RL) algorithms. As a novelty in model-based RL algorithms, a model predictive RL algorithm is proposed to reduce the number of iterations in the learning phase. A model-free reinforcement learning algorithm is utilised to obtain optimal control for tracking the reference online and without any knowledge of system dynamics. Finally, the simulation results verify the advantages of the proposed optimal control structure. [ABSTRACT FROM AUTHOR]

The synchronisation problem is studied for master–slave memristive neural networks (MNNs) in this paper. For alleviating the burden of communication bandwidth, a novel event-triggered scheme of data transmission is designed in the sensor-to-controller (S-C) channel. To deal with the unknown parameters and disturbances of master–slave MNNs, the adaptive controller is designed with the system states of triggering instants. Different from existing results about event-triggered adaptive control (ETAC) for MNNs, in which the event-triggered mechanism (ETM) is installed in the controller-to-actuator (C-A) channel, the event-triggered scheme in this paper is designed between the sensor and the controller, so the information flow of S-C channel is discontinuous. The adaptive laws can only use discrete-time system states transmitted at triggering instants to update control gains in this paper. By means of the Lyapunov methods, adaptive control theories and event-triggered techniques, sufficient conditions for synchronisation and quasi-synchronisation are obtained. At the same time, the designed ETM can avoid Zeno behaviour theoretically. Finally, the validity of the obtained results is shown by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper presents a new robust convergence condition of iterative learning control with initial state learning (ILC-ISL) for linear multivariable discrete-time systems in the presence of iteration-varying uncertainty. This method is based on linear matrix inequality (LMI) and provides fixed learning gains during time and iteration. Since the convergence of the ILC algorithm may change due to uncertainty in the parameters of a system, and the ILC algorithm is incapable of dealing with iteration-related challenges, it is a major challenge to reject the effect of iteration varying uncertainty. Besides, in the basic ILC algorithm, the initial state is constant in each iteration and consequently always leads to a tracking error. In this paper, first, a convergence condition of the ILC-ISL algorithm is designed based on closed-loop system stability in the iteration domain, and second, a new robust convergence condition is achieved by the LMI approach. Finally, the effectiveness of the proposed robust convergence scheme is evaluated through a numerical example and a mechanical system, respectively. [ABSTRACT FROM AUTHOR]

This paper is focusing on the stability analysis of aperiodic sampled-data systems. The augmented Lyapunov functional is powerful to produce a stability criterion with less conservatism owing to the well construction of coupled relationships among time-dependent states. In this paper, a novel augmented Lyapunov functional involving the time-squared-dependent augmented term is presented under the double-side looped-functional technique, which considers coupled relationships more fully than the current ones. Then, an improved negative definiteness lemma based on adjustable parameters is developed, resulting in a less conservative negative definite condition for the derivative of the Lyapunov functional. Finally, a stability criterion is derived based on the Lyapunov functional and the improved lemma, whose effectiveness is illustrated with four numerical examples and one practical example. [ABSTRACT FROM AUTHOR]

This paper extends the finite-time input-to-state stability (FTISS) issue to the discrete-time dynamical systems. Based on the Lyapunov method, sufficient conditions are derived to check the FTISS property of the discrete-time nonlinear systems with inputs. In addition, the generalised class- K L functions and the settling-time function capturing the finite settling-time behaviour of the dynamical system are constructed explicitly and well studied. In the end of the paper, a numerical example is provided to illustrate the feasibility/effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper discusses the output-feedback-based model-free optimal output tracking control problem of discrete-time systems with completely unknown system models under mild assumptions. The only information that allows utilisation is the system output and the reference output. To overcome these challenges, the paper aims to solve a model-free optimal output regulation problem for achieving optimal output tracking control; solving an optimal output regulation problem is equivalent to solving a linear quadratic regulation (LQR) problem and a constrained static optimisation problem. The state reconstruction is first given to represent the system state in terms of the input and output sequences. A data-driven value iteration (VI) algorithm is then proposed to iteratively approximate the solution to the discrete-time algebraic Riccati equation (ARE) of the corresponding LQR problem on the basis of input and output data. Next, based on the iterative solutions with respect to the ARE, a model-free solution is provided for the corresponding constrained static optimisation problem. Finally, an alternative reference system equivalent to the original reference system is established to avoid the requirement of having the knowledge of the reference system dynamics and the reference state. A numerical example is employed to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper studies disturbance estimation and compensation for discrete-time large-scale nonlinear descriptor systems with unknown measurement noises. Interval type-2 (IT-2) Takagi–Sugeno (T–S) fuzzy model is used to represent nonlinear dynamics, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the matrix of derivative state. First, by using a novel model transformation, the fuzzy representation in the derivative matrix is formulated into the linear one. Then, an augmented fuzzy observer is introduced to implement a synchronous estimation for the system state and the unknown measurement noise, which guarantees that reachable sets of the closed-loop system are bounded by a given ellipsoid. Moreover, a compensation-based controller is employed to remove or relieve the uncertainties induced by measurement noises. Finally, the validity of the obtained theories is testified by a numerical example. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the problem of designing locally stabilizing dynamic output feedback controllers and estimate the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. A realistic scenario is assumed where the control signal is subject to saturation, and the premise variables are partially or completely unmeasured, that is, not available for the control law. As a result, the fuzzy output controller can have a different number of fuzzy rules and a different set of membership functions from the T-S model. To obtain locally stabilizable conditions, we propose modeling the variation rate of the membership functions without using upper bounds, a new contribution in the context of output control of discrete-time T-S systems. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of local passivity and local feedback passivation of smooth discrete-time nonlinear systems by considering their piecewise affine approximations. Sufficient conditions are derived for local passivity and local feedback passivity. These results are then extended to systems that operate over Gilbert-Elliott type communication channels. One of the main features of the approach presented in this paper is that it allows us to design the controller by solving a few linear matrix inequalities (LMIs) that are subject to certain constraints. As a special case, results for feedback passivity of piecewise affine systems over a lossy channel are also derived. [ABSTRACT FROM AUTHOR]

This paper focuses on the consensus tracking control problem of multi-agent systems (MASs) with arbitrary adjacency weights instead of traditional nonnegative weights in a sampling setting. First, unlike Lemma 4 in Hu and Hong [2007. Leader-following coordination of MASs with coupling time delays. Physica A: Statistical Mechanics and its Applications, 374(2), 853-863], for MASs with arbitrary weights, the global reachability of the leader node is just a necessary but not a necessary and sufficient condition to guarantee the positive stability of matrix H. Hence, it's urgent for us to establish some positive stability criteria of matrix H first, which is a necessary condition for MASs to achieve consensus tracking. Simultaneously, we also solve the following problems successfully: which nodes should have direct connection with the leader? What's the range size of the leader adjacency coefficients? Then, some sufficient consensus tracking control conditions are obtained for MASs without time-delays and with time-delays by using matrix analysis method and perturbation theory, respectively. Finally, numerical examples are given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper studies the robust static output feedback control of discrete-time Markov jump systems considering that the mode of operation cannot be directly measured. It is assumed that the only available information concerning the main jump process comes from a detector, so that the jump and detector processes can be modelled as a hidden Markov model. Initially, it is considered that the system's dynamic matrix is subject to parametric uncertainties. By assuming a full row rank condition for the output matrix and employing a clusterisation technique for the state space of the hidden Markov model, it is derived a set of linear matrix inequalities (LMIs) that guarantees robust stability in the mean-square sense of the closed-loop system, as well as a bound on its H 2 norm. It is also shown that this design technique is linked to the bounded real lemma, so that a new set of LMIs conditions can be obtained for the 'pure' H ∞ control problem, which can be extended to cover the robust polytopic case. The paper is concluded with an illustrative example. [ABSTRACT FROM AUTHOR]

In real systems, control inputs are often constrained, and the constrained controllability problems are far more difficult to deal with than the unconstrained controllability ones. In this paper, we consider the constrained controllability problem of discrete-time bilinear systems. Specifically, we study the bounds of the control inputs for the systems to be controllable. Our approach is to first prove constrained near-controllability of a special class of bilinear system and then use constrained near-controllability to approximate constrained controllability of general bilinear systems. Based on this approach, we derive conditions for constrained controllability of the systems, where the upper bound of the control inputs can be easily computed. Algorithms and examples are provided to demonstrate the results of this paper. [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]

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfyH∞filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fault detection observer design for discrete spatially interconnected time-delay systems (SITSs) in finite frequency range. Firstly, a delay-dependent generalised Kalman–Yakubivich–Popov (GKYP) lemma for SITSs is proposed. Then, by the giving GKYP lemma, a distributed fault detection observer design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents both an observer/Kalman filter identification (OKID) method-based linear quadratic digital tracker (LQDT) and a new functional observer-based discrete equivalent input disturbance (EID) estimator, for unknown square/non-square singular sampled-data systems with unknown input and output disturbances. Initially, it is shown that even if the solution of the impulsive mode-free singular linear quadratic tracker problem exists, under some quite general conditions the tracker-based generalised algebraic Riccati equation (GARE) might have no solution. To overcome this issue, an innovative methodology that involves an introduced reduced-order equivalent proper regular model (EPRM) of the singular system is presented, to make the tracker-based GARE solvable for a wide class of servo control problems for a singular system. Furthermore, a new functional observer-based design methodology for the discrete EID estimator of the discrete EPRM is proposed in this paper, for a proper sampled-data system with unknown matched/mismatched input and output disturbances. Finally, a discrete-time EPRM of the unknown singular sampled-data system is constructed using the off-line OKID method and the robust prediction-based state-estimate optimal LQDT, associated with the (plug-in) discrete EID estimator, is developed for the singular sampled-data system. [ABSTRACT FROM AUTHOR]

Solving the optimal mean-field control problem usually requires complete system information. In this paper, a Q-learning algorithm is discussed to solve the optimal control problem of the unknown mean-field discrete-time stochastic system. First, through the corresponding transformation, we turn the stochastic mean-field control problem into a deterministic problem. Second, the H matrix is obtained through Q-function, and the control strategy relies only on the H matrix. Therefore, solving H matrix is equivalent to solving the mean-field optimal control. The proposed Q-learning method iteratively solves H matrix and gain matrix according to input system state information, without the need for system parameter knowledge. Next, it is proved that the control matrix sequence obtained by Q-learning converge to the optimal control, which shows theoretical feasibility of the Q-learning. Finally, two simulation cases verify the effectiveness of Q-learning algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose two successive heuristic iterative methods for inner-estimating domains of attraction for discrete-time non-polynomial systems. Firstly, we utilise a discrete-time fuzzy model to derive a piecewise difference inclusion for the discrete-time non-polynomial system. Then, an initial heuristic iterative method is presented to inner-estimate the domain of attraction as large as possible by first iteratively calculating common Lyapunov-like functions and then heuristically updating piecewise difference inclusions. Afterwards, the initial heuristic iterative method is further improved by piecewise Lyapunov-like functions, arriving at a refined heuristic iterative method. Especially, we introduce homotopy continuation method to decrease the computational complexity. At last, our methods are applied to three discrete-time non-polynomial examples with a brief discussion. [ABSTRACT FROM AUTHOR]

In this paper, the reduced-order H ∞ filtering problem for discrete-time singular systems under fading channels is studied. Our aim is to design a reduced-order filter to ensure the filtering error system with fading measurements is stochastically admissible and meets the given performance index. And the designed method is less conservative. However, the standard linear matrix inequality (LMI) cannot be obtained due to the nonlinear terms in decoupling. For this purpose, a new LMI is obtained by using new decoupling method. Finally, numerical example and electrical circuit example are given to clearly illustrate that the proposed method is less conservative than that of the existing method. [ABSTRACT FROM AUTHOR]

This paper considers a discrete-time stochastic optimal control problem for which only measurement equation is partially observed with unknown constant parameters taking value in a finite set of stochastic systems. Because of the fact that the cost-to-go function at each stage contains variance and the non-separability of the variance is so complicated that the dynamic programming cannot be successfully applied, the optimal solution has not been found. In this paper, a new approach to the optimal solution is proposed by embedding the original non-separable problem into a separable auxiliary problem. The theoretical condition on which the optimal solution of the original problem can be attained from a set of solutions of the auxiliary problem is established. In addition, the optimality of the interchanging algorithm is proved and the analytical solution of the optimal control is also obtained. The performance of this controller is illustrated with a simple example. [ABSTRACT FROM AUTHOR]

This paper deals with the filter design problem of two-dimensional (2-D) discrete-time nonlinear systems described by Fornasini-Marchesini local state-space (FM LSS) model under Takagi-Sugeno (T-S) fuzzy rules. The frequency of disturbance input is assumed to be known and to reside in a finite frequency (FF) range. A novel so-called FF gain is defined for 2-D discrete-time systems, which extends the standard gain. The aim of this paper is to design filters such that the filtering error system is asymptotically stable and has the disturbance attenuation performance in sense of FF gain. Sufficient conditions for the existence of a desired fuzzy filter are established in terms of linear matrix inequalities (LMIs). Simulation examples demonstrate the technique and its advantage. [ABSTRACT FROM AUTHOR]

In this paper, a novel dynamic surface control methodology with a predictive event-triggered strategy is proposed for discrete-time strict-feedback systems. In order to evaluate immeasurable state variables, a least square evaluation method is adopted. A dynamic surface controller is designed for discrete-time strict-feedback systems. When the transmission time of Sensor-to-Controller (S-C) or Controller-to-Actuator (C-A) channel increases, the stability and dynamic performance of the system deteriorates are improved by the proposed predictive event-triggered control strategy. Furthermore, the proposed methodology decreases the use of network resources while the whole system still keeps stable and exhibits an acceptable dynamic performance. The simulation results demonstrate that the proposed methodology is effective. [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]

This paper is concerned with the variance-constrained filtering problem for a class of discrete-time genetic regulatory networks (GRNs) with state delay and random one-step measurement delay. The phenomenon of the random one-step measurement delay is characterised by a random variable, which is assumed to obey the Bernoulli distribution with known occurrence probability. The purpose of the addressed problem is to design a filter such that, in the presence of state delay and random one-step measurement delay, an upper bound of the filtering error covariance matrix can be obtained and the explicit expression of the filter gain matrix is given. Then, the proposed variance-constrained filtering method can be used to approximate the concentrations of mRNAs and proteins. Finally, a numerical example is provided to illustrate the effectiveness of the designed filtering scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the design problem of observer-based control in finite frequency (FF) domain for discrete-time Takagi-Sugeno (T-S) fuzzy systems. With the aid of Generalised Kalman-Yakubovi-Popov (GKYP) lemma, new conditions guaranteeing the FF performance of the T-S fuzzy systems are derived in terms of Linear Matrix Inequalities. This study reduces the conservativeness of the existing design of the entire frequency range and includes it as special case. In the end, some examples are provided to illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability of impulsive discrete-time systems with infinite delays. Some sufficient conditions are obtained to guarantee the exponential stability of the considered systems by employing Lyapunov functions together with Razumikhin technique. Finally, three numerical examples are given to illustrate the effectiveness and superiority of the obtained results. It is the first time that the exponential stability of impulsive discrete-time systems with infinite delays is studied, the obtained results complement some recent works. [ABSTRACT FROM AUTHOR]

In this paper, a novel identification method for discrete-time linear systems when input-output observations are contaminated by coloured noise (errors-in-variables models) is proposed. To develop the new approach, modified prediction error and covariance matching methods are utilised. It is proved that the proposed approach leads to a consistent estimation. System identification through the proposed approach entails the existence of a flat frequency interval in power spectra of input and ratio of noise-free input to input signals which is a somewhat mild assumption. Two Monte Carlo simulations are provided to explain the efficiency, numerical complexity and the application of the proposed method. [ABSTRACT FROM AUTHOR]

This paper tackles the leader-following exponential consensus (LFEC) problem of nonlinear stochastic discrete-time multi-agent systems (DTMASs), which are subject to parameter uncertainties, stochastic disturbances and time-varying delay. An effective impulsive control strategy is utilised to guarantee that the leader-following consensus can be achieved exponentially. Particularly, several sufficient criteria regarding LFEC are derived by exploring the Lyapunov–Krasovskii functional and the linear matrix inequality technique. Additionally, the definition of the average impulsive interval is embedded into our developed results, which makes the results to be less conservative than those utilising the maximum and minimum impulsive intervals. At last, by the demonstration of numerical simulation results, the developed results are proven to be effective for achieving the LFEC of DTMASs. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the multi-rate sampled-data based exponential stabilisation problem of delayed Lur'e systems. First, a merging time sequence { t k } is constructed from the sampling instants of multiple sensors to form the so-called analysis interval and the closed-loop system is represented by a system with multiple time-varying delays over the constructed analysis interval. Then, a useful estimation about the norm of the system state is established. On this basis, a stabilisation criterion is proposed by constructing a two-sided looped-functional. The proposed functional drops positive definite restrictions over the whole analysis interval [ t k , t k + 1). Therefore, it can reduce the conservatism of the derived criterion. And, the feasible solution of the multi-rate sampled-data controller gain can be provided by solving a set of LMIs. Finally, the given example shows the advantage of the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the input-to-state stability (ISS) of nonlinear discrete-time time-varying impulsive delay systems with the coexistence of stabilising and destabilising impulses. Some ISS criteria are established for discrete-time impulsive delay systems by employing the Lyapunov functional where the coefficient of the estimated upper bound of the time difference of the Lyapunov functional is allowed to be a time-varying function which can take both negative and positive values. In addition, the ISS of a class of discrete-time linear time-varying impulsive delay systems is discussed by utilising a non-quadratic Lyapunov functional. Numerical examples are presented to verify the effectiveness of the main results. [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]

This paper investigates the convergence characteristics of the conventional P-type iterative learning control (ILC) scheme and exploits a gain-adaptive iterative learning control mechanism for a class of linear discrete-time singular systems. Based on the lifted vector technique, the paper reforms the discrete-time singular system as a kind of algebraic input-output transmission. For the conventional P-type ILC scheme, the asymptotical convergence in terms of the tracking-error vector is achieved and the monotonic convergence in the sense of 2-norm of the tracking-error vector is derived. Further, in order to improve the learning performance, a gain-adaptive iterative learning control (GAILC) strategy is developed, which argues the iteration-time-variable gain vector while minimising the increment of quadratic tracking-error vectors of two adjacent iterations. The existence of the optimal gain vector is explored through the optimisation criterion and the algebraic approach of the columns/ rows exchanging transformation of matrix. Then the non-conditionally strictly monotonic convergence of the GAILC is made by studying the eigenvalues of the quadratic function. Finally, the validity and the effectiveness of the P-type ILC are numerically demonstrated and the remarkable outcomes of the GAILC are illustrated. [ABSTRACT FROM AUTHOR]

This paper characterises and analyses the minimum detectable fault (MDF) (named generalised MDF here) for multiple multiplicative actuator faults based on set-separation constraints of healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, multiple multiplicative actuator faults are equivalently transformed into the form of multiple additive actuator faults for the sake of obtaining the simplified faulty residual set explicitly. Then, two different generalised MDF for different multiple actuator faults are, respectively, defined, which can be computed via solving simple linear programming (LP) problems. Moreover, we propose three detectability conditions to guarantee the detection of multiple multiplicative actuator faults by using the invariant set-based method. Finally, we provide effective selection guidance for the detection of different multiple multiplicative actuator faults by systematically analysing the conservatism and characteristics of these three guaranteed detectability conditions. At the end of this paper, an electrical circuit example is used to illustrate the effectiveness of the proposed method. [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 addresses stability and performance of sampled-data systems with variable sampling rate, where the change between sampling rates is decided by a scheduler. A motivational example is presented, where a stable continuous time system is controlled with two sampling rates. It is shown that the resulting system could be unstable when the sampling changes between these two rates, although each individual closed-loop system is stable under the designed controller that minimizes the same continuous loss function. Two solutions are presented in this paper. The first solution is to impose restrictions on switching sequences such that only stable sequences are chosen. The second solution presented is more general, where a piecewise constant state feedback control law is designed which guarantees stability for all possible variations of sampling rate. Furthermore, the performance defined by a continuous time quadratic cost function for the sampled-data system with variable sampling rate can be optimized using the proposed synthesis method. [ABSTRACT FROM AUTHOR]

This paper investigates model order reduction (MOR) methods of discrete-time systems via discrete orthogonal polynomials in the time domain. First, this system is expanded under discrete orthogonal polynomials, and the expansion coefficients are computed from a linear equation. Then the reduced-order system is produced by using the orthogonal projection matrix that is defined in terms of the expansion coefficients, which can match the first several expansion coefficients of the original output, and preserve the asymptotic stability and bounded-input/bounded-output (BIBO) stability. We also study the output error between the original system and its reduced-order system. Besides, the MOR method using discrete Walsh functions is proposed for discrete-time systems with inhomogeneous initial conditions. Finally, three numerical examples are given to illustrate the feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel stability analysis method for continuous-time linear systems with aperiodic sampling is presented by using a partitioned looped-functional approach. Based on the Lyapunov function with a new looped-functional, the stability condition is derived by using a bidirectional fragmentation of a sampling interval from t k to t k + 1 , which is divided into two sides forward and backward directions based on time t. For the bidirectional regions, the new looped functional is constructed by taking into account relations between states defined at the fragmented time and the sampling time. The improvement using the proposed scheme is shown through the comparisons with existing methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov-Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fault detection problem for two-dimensional (2-D) discrete-time systems described by the Fornasini–Marchesini local state-space model. The goal of the paper is to design a fault detection filter to detect the occurrence of faults in finite-frequency domain. To this end, a finite-frequencyH−index is used to describe fault sensitivity performance, and a finite-frequencyH∞index is used to describe disturbance attenuation performance. In light of the generalised Kalman–Yakubovich–Popov lemma for 2-D systems and matrix inequality techniques, convex conditions are derived for this fault detection problem. Based on these conditions, a numerical algorithm is put forward to construct a desired fault detection filter. Finally, a numerical example and an industrial example are given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

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]

In this paper, the finite-time memory fault detection filter (MFDF) is designed for nonlinear discrete systems with randomly occurring deception attacks, where the phenomenon of the randomly occurring deception attacks is characterised by a Bernoulli distributed random variable with known probability. To be specific, the finite-horizon data are employed to construct the MFDF. The main purpose of this paper is to design the MFDF such that, for all nonlinearities, external disturbances and randomly occurring deception attacks, the resultant augmented system is finite-time stable and attains the H ∞ performance. Accordingly, some sufficient conditions are developed to guarantee the existence of the desired fault detection filter parameters, where the solvability of the addressed problem is verified by the feasibility of certain matrix inequalities. Moreover, in order to show that the MFDF has better detection performance, a non-memory fault detection filter (NMFDF) is constructed to compare with the MFDF. Finally, two numerical simulations are utilised to illustrate the effectiveness of the proposed fault detection strategies and explain the superiority of the proposed MFDF. [ABSTRACT FROM AUTHOR]

This paper provides an analysis of uncertain discrete-time negative imaginary and positive real systems with state-space symmetry. First, a necessary and sufficient condition is provided for a minimal state-space symmetric system to be discrete-time positive real or discrete-time negative imaginary. Then, based on the discrete-time symmetric negative imaginary and positive real lemmas, bounds on symmetrically structured perturbations that maintain the negative imaginariness and positive realness of a discrete-time state-space symmetric system are derived. Finally, an RL network example is provided to illustrate the main results of the paper. [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 is concerned with the adaptive fuzzy control for uncertain switched discrete-time nonlinear systems in a pure-feedback form under arbitrary switchings. The design and the stability analysis of the adaptive fuzzy control with state constraints are based on the adaptive fuzzy backstepping control and the Lyapunov function. The feature of the proposed approach is as follows. (i) The proposed adaptive fuzzy control is designed by suppressing the explosion problem of the complexity in the backstepping control, (ii) In the fuzzy inference approach, the nonlinear uncertainties are approximated by using the fuzzy logic systems based on the simplified extended single-input rule modules, and (iii) The proposed estimator to take the estimates for the unmeasurable states, the adjustable parameters and the real control is in a simplified structure designed. The simulation experiment provides that the proposed approach improves the system performance. [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]

This paper presents a prescribed performance control for MIMO stochastic discrete-time nonlinear systems in a strict-feedback form using a set of noisy measurements. The prescribed performance control is proposed as follows. Transforming the un-constrained states into the constrained states, the proposed prescribed performance control with state constraints is designed based on the approach of backstepping control and the Lyapunov function without using approximate approaches. The nonlinear uncertainty is approximated as the fuzzy logic system based on the simplified extended single input rule modules to reduce the number of the fuzzy IF–THEN rules. The estimator to take the estimates for the unmeasurable states and the adjustable parameters is in a simplified structure designed. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system. [ABSTRACT FROM AUTHOR]

The saturation input control problem of discrete-time networked systems via adaptive event-triggered communication scheme is discussed in this paper. The criteria are derived by utilising a new Lyapunov functional to guarantee that the considered networked system with randomly occurring infinite distributed delays, random packet losses and sensor saturation is exponentially stable in mean square sense. A novel adaptive event-triggered law is proposed, which is dependent on the exponentially stable index α. The effectiveness of our proposed method is illustrated by both theoretical analysis and numerical simulations. [ABSTRACT FROM AUTHOR]