Robust stability of uncertain impulsive control systems with time-varying delay

In this paper, we are concerned with the robust stability problem of an uncertain impulsive control system with time-varying delay. By employing the formula for the variation of parameters and estimating the Cauchy matrix, several criteria on robust exponential stability are derived and the exponential convergence rate is estimated. Based on $P$-norm and $P$-measure of matrix, it is seen that our sufficient conditions are less restrictive than the ones in the earlier publication. Some numerical examples and simulations are given to illustrate the theoretical results and to show that the criteria can be applied to stabilize the unstable continuous system with time delays and uncertainties by utilizing impulsive control.     

Robust reliable control design for networked control system with sampling communication

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.     

Robust sampled-data control with random missing data scenario

The problem of robust sampled-data control for uncertain dynamic systems in the presence of missing data has been investigated. By using stochastic variables with a Bernoulli distributed white sequence to model missing data, along with time-varying norm-bounded uncertainties, and the input delay approach for sampled-data systems, two models for the considered sampled-data control system are proposed as the consecutive missing data scenario. Moreover, when data are missing, the control signals are held as the last received data. Sufficient conditions for the existence of desired robust sampled-data controllers are presented in the form of a linear matrix inequality. A numerical example is given to illustrate the validity of the proposed methods and to compare the results between the two proposed models of the sampled-data control system.     

Robust reliable control of uncertain nonlinear stochastic systems subject to actuator fault

This paper addresses the issue of robust reliable stabilization for a class of uncertain nonlinear stochastic systems with both discrete and distributed time-varying delays and possible occurrence of actuator faults. By constructing a new Lyapunov functional and using linear matrix inequality technique, a new set of sufficient conditions is established for the stochastic stability of the uncertain nonlinear stochastic systems. Then, sufficient conditions are obtained for the solvability of the robust stabilization problem via robust reliable controller. More precisely, the derived control law guarantees the robust stabilization of nonlinear stochastic systems in the presence of known actuator failure matrix and uncertainties. Further, the results are extended to study the stabilization of stochastic systems with unknown actuator failure matrix. Moreover, the obtained criteria are formulated in terms of LMIs and also the reliable controller can be designed in terms of the solutions to certain linear matrix inequalities. Finally, numerical examples with simulation result are presented to demonstrate the validity and less conservatism of the obtained results.     

基于观测器的网络切换模糊时滞系统鲁棒控制

针对带有随机时变时滞的非线性网络切换系统稳定控制问题进行研究,在系统状态不可测且存在不确定性的情况下,采用T-S模型将非线性网络切换系统建模为网络切换模糊系统。然后,采用平均驻留时间法（ADT）,设计出基于观测器的控制器及系统切换律,并给出网络切换模糊系统指数稳定的平均驻留时间条件。结合李雅普诺夫（LKF）方法给出时滞相关的网络切换模糊系统指数稳定的矩阵不等式条件。最后通过MATLAB数值仿真验证了该设计方法的有效性和优越性。     

Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

带有时变时滞和不确定性拓扑的双积分系统的一致性

研究带有不确定性拓扑的双积分系统在有时滞的情况下的一致性问题,通过线性矩阵不等式的方法,得到一致性的充分条件。本文最大的贡献是考虑双积分系统,在有不确定性信息和时变时滞的情况下,找出控制协议使其一致。最大合适的时变时滞和不确定性可以由线性矩阵不等式得到。最后给出仿真,证明定理的有效性。     

Synchronization for general complex dynamical networks with sampled-data

In this paper, the sampled-data synchronization control problem is investigated for a class of general complex networks with time-varying coupling delays. A rather general sector-like nonlinear function is used to describe the nonlinearities existing in the network. By using the method of converting the sampling period into a bounded time-varying delay, the addressed problem is first transformed to the problem of stability analysis for a differential equation with multiple time-varying delays. Then, by constructing a Lyapunov functional and using Jensen's inequality, a sufficient condition is derived to ensure the exponential stability of the resulting delayed differential equation. Based on that, the desired sampled-data feedback controllers are designed in terms of the solution to certain linear matrix inequalities (LMIs) that can be solved effectively by using available software. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed sampled-data control scheme.     

执行器失效不确定时滞系统的指定衰减度鲁棒可靠控制

针对一类含有时变时滞的不确定参数线性系统,研究了在执行器发生故障情况下的鲁棒可靠控制器设计问题.系统中的参数不确定性满足广义匹配条件,时变时滞的大小及其变化率有界,并假设故障执行器元件的输出为零.经过适当的模型变换,将原系统的鲁棒指数镇定问题转化为另一个等价系统的鲁棒镇定问题.根据Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,分别给出了鲁棒可靠控制器存在的时滞无关和时滞相关充分条件.仿真结果表明了该控制器设计方法的有效性.     

Dissipative based adaptive reliable sampled-data control of time-varying delay systems

This paper is concerned with the problem of dissipative based adaptive reliable controller for a class of time delay systems subject to actuator failures and time-varying sampling with a known upper bound on the sampling intervals. By constructing a proper Lyapunov-Krasovskii functional which fully uses the available information about the actual sampling pattern and time delays, a new set of sufficient conditions is derived to obtain the required result. Then, a dissipative based adaptive sampled-data controller is designed such that the resulting closed-loop system is reliable in the sense that it is asymptotically stable and has the prescribed dissipative performance under given constraints. The existence condition of the desired dissipative based adaptive reliable sampled-data controller is obtained in terms of linear matrix inequalities. Further, the performance of the proposed controller is implemented on a liquid propellant rocket motor with a pressure feeding system model. The simulation results show the effectiveness and better performance of the proposed adaptive reliable sampled-data controller over conventional reliable controller.     

Exponential stabilisation for time-varying delay system with actuator faults: an average dwell time method

The issue of exponential stabilisation for a class of special time-varying delay switched systems resulting from actuator faults is considered in this article. The time-varying delay is assumed to belong to an interval and can be a slow or fast time-varying function. A hybrid state feedback strategy is redesigned to guarantee the system stable since the original controller is unavailable for some actuators failures. A class of switching laws incorporating the average dwell time method is proposed so that the special switched system with interval time-varying delay is exponentially stable. New delay-range-dependent stabilisation conditions using state feedback controllers are formulated in terms of linear matrix inequalities (LMIs) by choosing appropriate Lyapunov–Krasovskii functional without neglecting some useful knowledge on system states. Parameterised characterisations of the controllers are given in terms of the feasibility solutions to the LMIs. Two numeral examples are given to demonstrate the applicability and the effectiveness of the proposed method.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

Distributed guaranteed cost control for aperiodic sampled-data networked interconnected systems: a switched system approach

This paper investigates the distributed guaranteed cost control problem for a class of networked interconnected control systems (NICSs) under aperiodic sampling. The NICSs with missing data and time-varying delay are modelled as an aperiodic sampled-data switched system with uncertainties. Then, sufficient conditions ensuring the exponential stability and guaranteed cost quadratic performance are presented by using the average dwell time approach. The distributed state feedback controller is designed by solving a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Exponential stabilisation of memristive neural networks under intermittent output feedback control

In this paper, the exponential stabilisation problem is studied for a general class of memristive time-varying delayed neural networks under periodically intermittent output feedback control. First, the periodically intermittent output feedback control rule is designed for the exponential stabilisation of the memristive time-varying delayed neural networks. Then, we derive stabilisation criteria so that the memristive time-varying delayed neural networks are exponentially stable. By the mathematical induction method and constructing suitable Lyapunov–Krasovskii functionals, some easy-to-check criteria are obtained to ensure the exponential stabilisation of memristive time-varying delayed neural networks. Finally, two numerical simulation examples are given to illustrate the validity of the obtained results.     

Robust extended dissipative control for sampled-data Markov jump systems

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.     

线性不确定时滞系统的时滞依赖鲁棒镇定方法研究

研究一类同时存在状态和控制滞后的线性不确定时滞系统的鲁棒镇定问题。系统的不确定项参数时为未知但范数有界,其滞后项也时时变的。对此,给出一个使得系统鲁棒稳定的无记忆状态反馈控制律,所得结果与时滞相关,且相应的结果以线性矩阵不等式的形式给出。     

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay.Some Lyapunov-Krasovskii functionals are constructed and the linear matrix inequality(LMI)approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence,uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties.By using Leihniz-Newton formula,free weighting matrices are employed to express this relationship,which implies that the new criteria are less conservative than existing ones.Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems

In this paper, we consider the H/sub 2/ sampled-data control for uncertain linear systems by the impulse response interpretation of the H/sub 2/ norm. Two H/sub 2/ measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H/sub 2/ criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.