Robust Stability and $$H_{\infty }$$ Control of Discrete-Time Uncertain Impulsive Systems with Time-Varying Delay

This paper considers the robust stability and \(H_{\infty }\) control problems for a class of discrete-time uncertain impulsive systems with time-varying delay. Sufficient conditions for the robust stability, stabilization and \(H_\infty \) control of the considered systems are developed. Some numerical examples are presented to show the effectiveness of the theoretical results.     

Robust \mathcal{H}_{\infty} State Feedback Control of Networked Control Systems with Congestion Control

This paper examines the problem of robust state feedback control of networked control systems with a simple congestion control scheme. This simple congestion control scheme is based on comparing current measurements with last transmitted measurements. If their difference is less than a prescribed percentage of the current measurements then no measurement is transmitted to the controller. The controller always uses the last transmitted measurements to control the system. With this simple congestion control scheme, a robust $\mathcal {H}_{\infty}$ state feedback controller design methodology is developed based on the Lyapunov–Krasovskii functional approach. Sufficient conditions for the existence of delay mode dependent controllers are given in terms of bilinear matrix inequalities (BMIs). These BMIs are converted into quasi-convex linear matrix inequalities (LMIs) and solved by using the cone complementarity linearization algorithm. The effectiveness of the simple congestion control in terms of reducing the network bandwidth is elaborated using simulation examples.     

$$H_{\infty }$$ Performance Analysis of 2D Continuous Time-Varying Delay Systems

This paper deals with the problem of \(H_{\infty }\) performance analysis of 2D continuous time-varying delay systems described by Roesser model. Using a simple Lyapunov–Krasovskii functional, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained result is then extended to the problem of \(H_{\infty }\) performance analysis. Several examples are provided in order to illustrate the effectiveness of our results.     

Reliable $$H_{\infty }$$ Stabilization of Fuzzy Systems with Random Delay Via Nonlinear Retarded Control

In this paper, the robust reliable \(H_\infty \) control problem has been investigated for a class of nonlinear discrete-time TS fuzzy systems with random delay. In particular, the proposed fuzzy system consists of local nonlinear models with set of fuzzy rules, but the conventional TS fuzzy systems has local linear models. Our attention is focused on the design of a feedback reliable nonlinear retarded control law to ensure the robust asymptotic stability for nonlinear discrete-time TS fuzzy system with admissible uncertainties as well as actuator failure cases and random delay. In particular, by using an input delay approach, the random delay with stochastic parameters in the system matrices is introduced in the system model. Based on the Lyapunov approach, firstly, a sufficient condition for asymptotic stability is proposed for TS fuzzy systems in the presence of actuator failures. Then, a robust reliable \(H_\infty \) control is designed for the uncertain TS fuzzy system by solving a strict linear matrix inequalities using the available numerical software. Finally, a numerical example based on real-time ball and beam system is provided to validate the effectiveness of the proposed design technique.     

Non-Fragile H_{\infty } Filter Design for Uncertain Stochastic Nonlinear Time-Delay Markovian Jump Systems

This paper investigates the problem of non-fragile and mode-dependent \(H_{\infty }\) filter design for a class of nonlinear stochastic Markovian jump systems with mode-dependent time-varying delays and norm-bounded parameter uncertainties. The non-fragile and mode-dependent filter to be designed is assumed to include multiplicative gain variations which result from inaccuracies in filter implementation, and the desired filter ensures the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed \(H_{\infty }\) -norm level for all admissible uncertainties. A stochastic Lyapunov–Krasovskii function is proposed to reflect the information of Markovian jump modes and the mode-dependent time-varying delays, and a set of strict linear matrix inequalities are utilized to derive sufficient conditions that guarantee the desired filter can be constructed. A numerical example and a vertical take-off and landing (VTOL) helicopter system are utilized to illustrate the effectiveness and usefulness of the main results obtained.     

Stability and $${L_{\infty }}$$-Gain Analysis for Positive Switched Systems with Time-Varying Delay Under State-Dependent Switching

This paper investigates the problems of stability and \({L_\infty }\)-gain analysis for a class of positive switched systems with time-varying delay. Attention is focused on designing a state-dependent switching rule such that the system satisfies a prescribed \({L_\infty }\)-gain performance level, where the proposed scheme does not require the switching instants to be known in advance. By constructing an appropriate co-positive type Lyapunov–Krasovskii functional, sufficient conditions for exponential stability with \({L_\infty }\)-gain performance of the underlying systems are derived. Furthermore, the stability along the switching surface is analyzed. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Robust H_{\infty } filtering for uncertain two-dimensional continuous systems with time-varying delays

This paper deals with the problem of delay-dependent robust $H_{\infty }$ H ∞ filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type. A sufficient condition for $H_{\infty }$ H ∞ noise attenuation is derived in terms of linear matrix inequalities, so a robust $H_{\infty }$ H ∞ filter can be obtained by solving a convex optimization problem. Finally, some examples are provided to illustrate the effectiveness of the proposed methodology.     

Quantized Feedback Adaptive Reliable $$H_{\infty }$$ Control for Linear Time-Varying Delayed Systems

Based on an improved \(H_\infty \) performance index, the method of designing a reliable adaptive \(H_\infty \) controller with quantized state is addressed for the time-varying delayed system in this paper. On the basis of online estimates of actuator faults, the controller parameters are updated automatically to compensate the influence of actuator faults on the system while the desired improved \(H_\infty \) performance is preserved. A Lyapunov function candidate is constructed to prove that the closed-loop system is asymptotically stable. And the existing sufficient conditions of the controller are proved to be less conservative. The gains of the controller and the parameters of the adaptive law are co-designed and obtained in terms of solutions to a set of linear matrix inequalities. Finally, two numerical examples are given to illustrate that the proposed method is more effective than the previous methods for time-varying delayed systems.     

\mathcal{H}_{\infty} Control Synthesis for Short-Time Markovian Jump Continuous-Time Linear Systems

In many actual engineering applications, the Markovian jump among subsystems often occurs in some short finite-time intervals. For this class of Markovian jump systems, called short-time Markovian jump systems in this paper, the state boundedness during the short-time Markovian jump interval is of great interest. By introducing the concepts of finite-time stochastic stability and boundedness, sufficient conditions ensuring short-time Markovian jump system to be $\mathcal{H}_{\infty}$ finite-time stochastic bounded are derived. Then, the control synthesis problem is studied, where both asymptotic stability and finite-time stochastic boundedness are considered. Finally, an LMI-based design algorithm is proposed to solve the control synthesis problem. Several numerical examples are given to illustrate the results proposed in this paper.     

Analysis and Design of $$H_{\infty }$$ Controllers for 2D Singular Systems with Delays

The \(H_{\infty }\) control design problem is solved for the class of 2D discrete singular systems with delays. More precisely, the problem addressed is the design of state-feedback controllers such that the acceptability, internal stability and causality of the resulting closed-loop system are guaranteed, while a prescribed \(H_\infty \) performance level is simultaneously fulfilled. By establishing a novel version of the bounded real lemma, a linear matrix inequality condition is derived for the existence of these \(H_\infty \) controllers. They can then be designed by solving an iterative algorithm based on LMI optimizations. An illustrative example shows the applicability of the algorithm proposed.     

Extended Robust \mathcal{H}_{2} and \mathcal{H}_{\infty} Filter Design for Discrete Time-Invariant Linear Systems with Polytopic Uncertainty

This paper is concerned with the problem of robust $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ filter design for discrete-time linear time-invariant systems with polytopic parameter uncertainties. Less conservative robust $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ filter design procedures are proposed in terms of single-parameter minimization problems with linear matrix inequality constraints. To this end, we generalize the filter structures available in the literature to date in such a way that the filter’s next state is built by summing the filter’s states over several samples from the past to the present. For stability of the filtering error system, the homogeneous polynomial parameter-dependent Lyapunov functions are employed. Finally, illustrative examples are given to demonstrate the merits of the proposed methods.     

Robust Output-Feedback Control for Linear Continuous Uncertain State Delayed Systems with Unknown Time Delay

The state-delayed time often is unknown and independent of other variables in most real physical systems. In this paper, a new stability criterion for uncertain systems with a state time-varying delay is proposed. Then, a robust observer-based control law based on this criterion is constructed via the sequential quadratic programming method. We also develop a separation property so that the state feedback control law and observer can be independently designed and maintain closed-loop system stability. An example illustrates the availability of the proposed design method.     

\mathcal{H}_{\infty} Filtering for Short-Time Switched Discrete-Time Linear Systems

In this paper, the $\mathcal{H}_{\infty}$ filtering problem for a class of short-time switched discrete-time linear systems is investigated. For such systems, switching always occurs in some short interval. Since the error state may attain large unacceptable values in short-time switching intervals, besides the asymptotic stability of error dynamics, the boundedness of error state is also significant for short-time switched systems. Thus the designed filter is composed of two parts: asymptotic filter, based upon the existing results, ensures the asymptotic stability of the system during normal, relatively long interval, and finite-time filter ensures system to be finite-time bounded during the short interval of switching, which is the main concern in this paper. By introducing the concept of finite-time boundedness, the proposed filter is formulated as a set of sub-filters ensuring the error dynamics $\mathcal{H}_{\infty}$ finite-time bounded in the short switching interval. Finally, a numerical example is provided to illustrate the effectiveness of this approach.     

区间变时滞不确定系统鲁棒稳定性分析

本文针对一类线性区间变时滞不确定系统的鲁棒稳定性分析问题进行了研究.基于时滞中点法和凸组合技术,借助于构造一个包含四重积分项的新Lyapunov-Krasovskii（L-K）泛函,并利用积分不等式方法给出了LMI（Linear Matrix Inequality）形式的时滞相关稳定性新判据.与已有文献相比,该判据能大大降低理论推导和计算上的复杂性.最后通过三个具有代表性的数值例子对比验证了本文所提出方法在降低结论保守性方面的优越性.