Input‐to‐state exponents and related ISS for delayed discrete‐time systems with application to impulsive effects

This paper aims to investigate the input‐to‐state exponents (IS‐e) and the related input‐to‐state stability (ISS) for delayed discrete‐time systems (DDSs). By using the method of variation of parameters and introducing notions of uniform and weak uniform M‐matrix, the estimates for 3 kinds of IS‐e are derived for time‐varying DDSs. The exponential ISS conditions with parts suitable for infinite delays are thus established, by which the difference from the time‐invariant case is shown. The exponential stability of a time‐varying DDS with zero external input cannot guarantee its ISS. Moreover, based on the IS‐e estimates for DDSs, the exponential ISS under events criteria for DDSs with impulsive effects are obtained. The results are then applied in 1 example to test synchronization in the sense of ISS for a delayed discrete‐time network, where the impulsive control is designed to stabilize such an asynchronous network to the synchronization.     

Input‐to‐state stability for discrete‐time nonlinear impulsive systems with delays

This paper aims to study the problem of input‐to‐state stability (ISS) for nonlinear discrete impulsive systems with time delays. Razumikhin‐type theorems, which guarantee ISS – asymptotically ISS and exponentially ISS – for the discrete impulsive ones with external disturbance inputs, are established. As applications, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

A novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.     

Decentralized networked control of discrete‐time systems with local networks

This paper considers discrete‐time large‐scale networked control systems with multiple local communication networks connecting sensors, controllers, and actuators. The local networks operate asynchronously and independently of each other in the presence of variable sampling intervals, transmission delays, and scheduling protocols (from sensors to controllers). The time‐delay approach that was recently suggested to decentralized stabilization of large‐scale networked systems in the continuous time is extended to decentralized control in the discrete time. An appropriate Lyapunov‐Krasovskii method is presented that leads to efficient LMI conditions for the exponential stability and l₂‐gain analysis of the closed loop large‐scale system. Differences from the continuous‐time results are discussed. A numerical example of decentralized control of 2 coupled cart‐pendulum systems illustrates the efficiency of the results.     

Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete‐time state observations

This study investigates the stabilization issue of stochastic coupled systems with Markovian switching via feedback control. A state feedback controller based on the discrete‐time observations is applied for the stabilization purpose. By making use of the graph theory and the Lyapunov method, we establish both Lyapunov‐ and coefficient‐type sufficient criteria to guarantee the stabilization in the sense of stability, and then, we further develop the mean‐square asymptotical stability. In particular, the upper bound of the duration between 2 consecutive state observations is well formulated. Applications to a concrete stabilization problem of stochastic coupled oscillators with Markovian switching and some numerical analyses are presented to illustrate and to demonstrate the easy verifiability, effectivity, and efficiency of our theoretical findings.     

‐Gain analysis of event‐triggered networked control systems: a discontinuous Lyapunov functional approach

In this paper, the problems of exponential stability and ‐gain analysis of event‐triggered networked control systems (NCSs) with network‐induced delays are studied. We first propose event‐triggering conditions in the sensor side and controller side, respectively. Because the implementation of our event‐triggering scheme only needs periodic supervision of the system state at the constant sampling instants, instead of being monitored continuously, it is expected that the scheme will improve the resource utilization. Taking the network‐induced delays into account and using delay system approach, we constructed a unified model of NCSs with hybrid event‐triggering schemes. On the basis of this model, sufficient conditions for the exponential stability and ‐gain analysis are developed in the form of LMIs by using a discontinuous Lyapunov–Krasovskii functional approach. Moreover, the corresponding results can be further extended to more general cases, where the system matrices of the considered plant contain parameter uncertainties, represented in either polytopic or norm‐bounded frameworks. In addition, as a special case, we also present the exponential stability, ‐gain analysis, and the control feedback gain design of event‐triggered NCSs without considering the effects of network‐induced delays and event‐triggering condition in the controller side. Finally, a simulation example is provided to illustrate the usefulness and effectiveness of the proposed hybrid event‐triggering schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

Fault estimation for discrete‐time switched nonlinear systems with discrete and distributed delays

This paper is concerned with the fault estimation for a class of discrete‐time switched nonlinear systems with mixed time delays. The fault existing in the system is assumed to be characterized by an external system, which incorporates the fault's prior knowledge to the considered systems. The fault estimator is designed by using the multiple Lyapunov–Krasovskii functional and average dwell‐time approach. Sufficient conditions in the form of linear matrix inequalities (LMIs) are developed to ensure the resulting error system is exponentially stable with an optimized disturbance attenuation level. The gain matrices of the estimator can be easily determined by using the standard optimization toolboxes. Finally, numerical examples and simulation results with the help of real‐time systems are given to illustrate the effectiveness and advantages of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

This paper addresses the passivity‐based control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Stability and stabilization for stochastic Cohen‐Grossberg neural networks with impulse control and noise‐induced control

By applying the It formula, the Gronwall inequality, and the law of large numbers technique, a new simple sufficient inequality condition is presented for the almost surely exponential stability of the stochastic Cohen‐Grossberg neural networks with impulse control and time‐varying delays. Moreover, a new result is also given for the existence of unique states of the systems. An impulsive controller and a suitable noise controller are also given at the same time. The condition contains and improves some of the previous results in the earlier references.     

State and output feedback control of time‐delay switched linear systems

In this paper, we propose contributions on the stabilization and control of switched linear systems subject to time‐delays through the assignment of the switching law. As a first step, based on previous results related to switched linear systems with no time‐delays and exploiting the concept of piecewise quadratic Lyapunov–Krasovskii functionals, we solve the problem of finding suitable state‐dependent switching laws ensuring the prescribed control objectives. Secondly, we extend such results and present a strategy to construct an output feedback switching law, based on the available measurements made on the system. In both cases, the design of the control strategy is done by computing a feasible solution to a set of matrix inequalities associated to the modes of the switched linear system. Copyright © 2011 John Wiley & Sons, Ltd.     

and control design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper investigates the problems of and state feedback control design for continuous‐time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi‐simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter‐dependent Lyapunov matrices to certify the mean square closed‐loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with and state feedback control in both mode‐independent and mode‐dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

This paper focuses on the problem of finite‐time $H_{\infty }$ control for one family of discrete‐time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete‐time close‐loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite‐time boundedness and sliding mode $H_{\infty }$ finite‐time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

This paper deals with the problem of exponential filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods.     

Discrete‐time sector based hands‐off control for nonlinear system

This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time sector.” The design method to define the boundary of a discrete‐time sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.     

Semiglobal finite‐time synchronization of complex networks with stochastic disturbance via intermittent control

This paper focuses on the problem of semiglobal finite‐time synchronization of stochastic complex networks via an intermittent control strategy. By establishing a finite‐time criterion condition and a novel finite‐time ‐operator differential inequality, combined with convex techniques, some sufficient conditions are obtained to ensure finite‐time synchronization for stochastic complex networks with time delays. An effective controller is given to guarantee inner finite‐time synchronization, especially for a nondelayed dynamic system. This paper provides a simple controller. Finally, a numerical simulation is given to demonstrate the effectiveness of our results.     

Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

This paper focuses on the graphical tuning method of fractional order proportional integral derivative (FOPID) controllers for fractional order uncertain system achieving robust ‐stability. Firstly, general result is presented to check the robust ‐stability of the linear fractional order interval polynomial. Then some alternative algorithms and results are proposed to reduce the computational effort of the general result. Secondly, a general graphical tuning method together with some computational efficient algorithms are proposed to determine the complete set of FOPID controllers that provides ‐stability for interval fractional order plant. These methods will combine the results for fractional order parametric robust control with the method of FOPID ‐stabilization for a fixed plant. At last, two important extensions will be given to the proposed graphical tuning methods: determine the ‐stabilizing region for fractional order systems with two kinds of more general and complex uncertainty structures: multi‐linear interval uncertainty and mixed‐type uncertainties. Numerical examples are followed to illustrate the effectiveness of the method. Copyright © 2015 John Wiley & Sons, Ltd.     

Observer‐based fault estimators using iterative learning scheme for nonlinear time‐delay systems with intermittent faults

This paper deals with the intermittent fault estimation problem for a class of nonlinear time‐delay systems with measurement noise. The time delays are assumed to occur in state vector, nonlinear term as well as output vector, thus reflecting the time delays influence in reality more closely. The aim of the problem is to estimate the intermittent fault by using iterative learning scheme, with the property of index, hence attenuating the influence from measurement noise. Different from existing fault estimating schemes, the state error information and fault estimating information in the previous iteration are used in the current iteration to improve the estimating results. The stability and convergence of iterative learning observer and uniform boundedness of dynamic error system are achieved by using Lyapunov function and optimal function design. Simultaneously, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality by the Schur complements and Young relations. Furthermore, the results are both suited for the systems with time‐varying delay and the systems with constant delay. Finally, two numerical examples are proposed to illustrate the effectiveness of the proposed method, and a comparability example is presented to demonstrate its superiority. Copyright © 2017 John Wiley & Sons, Ltd.     

A less conservative approach to handle time‐varying parameters in discrete‐time linear parameter‐varying systems with applications in networked control systems

This article proposes a new strategy to deal with linear parameter‐varying discrete‐time systems, whose time‐varying parameters can be written as solutions (such as exponential, trigonometric, or periodic function) of a linear difference equation (DE). The novelty is to explicitly exploit the precise knowledge of the function describing the time‐varying parameter by incorporating the associated DE in the conditions, providing less conservative results when compared with conventional approaches based on bounded or arbitrary rates of variation. The advantage of the method comes from the fact that, differently from the available methods, the pointwise stability for the whole domain of the time‐varying parameters is not a necessary condition to obtain feasible solutions. The applicability and benefits of the proposed technique are investigated in terms of numerical examples concerning robust stability analysis,  filtering, and  state‐feedback control. As a final contribution, the problem of time‐varying sampling periods in the context of networked control systems is investigated using the proposed strategy. A numerical example based on a practical application is presented to illustrate the superiority of the approach when compared to methods from the literature based on matrix exponential computation.