Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.     

Stability independent of delay using rational functions

This paper is concerned with the problem of assessing the stability of linear systems with a single time-delay. Stability analysis of linear systems with time-delays is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we show that a linear system with a single time-delay is stable independent of delay if and only if a certain rational function parameterized by an integer k and a positive real number T has only stable roots for any finite T≥0 and any k≥2. We then show how this stability result can be further simplified by analyzing the roots of an associated polynomial parameterized by a real number δ in the open interval (0,1). The paper is closed by showing counterexamples where stability of the roots of the rational function when k=1 is not sufficient for stability of the associated linear system with time-delay. We also introduce a variation of an existing frequency-sweeping necessary and sufficient condition for stability independent of delay which resembles the form of a generalized Nyquist criterion. The results are illustrated by numerical examples.     

Control of a magnetic levitation system with communication imperfections: A model-based coupling approach

This work presents a control strategy to control a magnetic levitation system under the influence of coupling imperfections (disturbances). To overcome problems arising whenever the interconnections between plant and controller have a non-negligible influence on the control-loop behavior a so-called model-based coupling approach is used. The main idea of this coupling approach is to use prediction schemes based on recursively identified plant and controller models which compensate for performance degradation due to coupling imperfections. Coupling failures such as time-delays, data-losses and noise drastically influence the control-loop performance. Especially when systems in form of real hardware (real-time systems) are present such disturbances have to be handled adequately. To demonstrate the effectiveness of the model-based coupling approach, a control-loop of a magnetic levitation system is analyzed in simulation as well as in real world laboratory setup (HiL simulation). Furthermore a first insight into the stability analysis of closed-loop systems including the model-based coupling technique is performed for a simplified configuration.     

Robust H-infinity filtering for time-delay systems with missing measurements： a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.     

Effects of small delays on stability of singularly perturbed systems

A small delay in the feedback loop of a singularly perturbed system may destabilize it; however, without the delay, it is stable for all small enough values of a singular perturbation parameter ε. Sufficient and necessary conditions for preserving stability, for all small enough values of delay and ε, are obtained in two cases: in the case of delay proportional to ε and in the case of independent delay and ε. In the second case, the sufficient conditions are given in terms of an LMI. A delay-dependent LMI criterion for the stability of singularly perturbed differential-difference systems is derived.     

New H∞ control approaches for interval time-delay systems with disturbances and their applications

In this paper, the H_∞ performance and control problems for linear systems with interval state or input delays and disturbances are investigated. In order to exploit more information on the delay range, the quadruple -integral terms and quadratic forms of triple integrals are introduced into the Lyapunov-Krasovskii functional (LKF). Particularly, an improved integral inequality is developed for estimation of the cross terms in triple-integral type, which displays significant improvement over the Wirtinger inequality. As a result, a less conservative H_∞ performance criterion is derived without requiring many slack variables. Based on the criterion, the H_∞ controller design approaches are obtained. Besides the numerical examples, the applications to the practical systems are also provided to illustrate the effectiveness of the proposed approaches.     

线性定常中立型大系统的稳定性

本文讨论了线性定常中立型大系统的稳定性,得到了若干充分判据。我们对中立项的处理不同于已有的方法,另外找到了x_i(t-τ)与x_i(t-τ)的转换途径,为这类问题研究给出了一种新方法。     

Leader-following consensus of multi-agent systems with switching topologies and time-delays

This paper investigates the leader-following consensus problem of multi-agent systems where the leader is static and the controlling effect of each follower depends on its own state. The control protocols are proposed for two cases: i) for network with switching topologies and undirected information flow; ii) for network with directed information flow and communication time-delays. With the aid of several tools from algebraic graph, matrix theory and stability theory, the sufficient conditions guaranteeing leader-following consensus are obtained by constructing appropriate Lyapunov functions. Simulations are presented to demonstrate the effectiveness of our theoretical results.     

A switched system approach to stabilization f networked control systems

A switched system approach is proposed to model networked control systems (NCSs) with communication constraints. This enables us to apply the rich theory of switched systems to analyzing such NCSs. Sufficient conditions are presented on the stabilization of NCSs. Stabilizing state/output feedback controllers can be constructed by using the feasible solutions of some linear matrix inequalities (LMIs). The merit of our proposed approach is that the behavior of the NCSs can be studied by considering switched system without augmenting the system. A simulation example is worked out to illustrate the effectiveness of the proposed approach.