Stability and stabilization of continuous-time singular hybrid systems

In this paper, the problems of stability and state feedback stabilization for a class of continuous-time singular hybrid systems are investigated. A new sufficient and necessary condition for a continuous-time singular hybrid system to be regular, impulse-free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Moreover, a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.     

Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems

This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities (LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.      

Robust admissibility of uncertain switched singular systems

This article investigates the robust admissibility of uncertain discrete-time switched singular systems. First, the admissibility is introduced, by using the switched Lyapunov function, for singular systems. Sufficient conditions for robust admissibility of uncertain switched singular systems are presented in strict linear matrix inequalities formulation. Robust admissibility condition designs for both state feedback and static output control feedback are then derived. Numerical examples are provided to illustrate our approach.     

Stabilisation and control synthesis of switching systems subject to actuator saturation

This article presents sufficient conditions for the stabilisation of switching discrete-time linear systems subject to actuator saturations. These conditions are obtained by using successively state and output feedback control laws. The obtained results are formulated in terms of linear matrix inequalities (LMIs). The saturating and non-saturating controllers are synthesised for both cases in this work. Three sets of LMIs are presented for output feedback case. Numerical examples are used to illustrate these techniques by using a linear optimisation problem subject to LMI constraints.     

广义系统的时滞依赖静态输出反馈控制

针对一类不确定线性广义时滞系统,给出了静态输出反馈控制器的设计方法.首先基于标称广义时滞系统的稳定条件,以受限线性矩阵不等式形式,给出闭环广义时滞系统正则、无脉冲且渐近稳定的充分条件,同时利用受限矩阵不等式的可行解给出静态输出反馈控制律的一个参数化表示;其次,利用矩阵的正交补,把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式(LMIs)的可行解;最后应用数值实例说明了所给方法的有效性和正确性.     

Dissipative control and filtering of discrete-time singular systems

In this paper, the problems of dissipative control and filtering of discrete-time singular systems are investigated. Based on parametrising the solutions of the constraint set, a necessary and sufficient condition is established in terms of strict linear matrix inequality which makes the condition more tractable. By using the system augmentation approach, a static output feedback controller design method is proposed to guarantee that the closed-loop system is admissible and strictly (Q, S, R) dissipative. Then, the result is applied to tackle the reduced-order filtering problem. The effectiveness of the obtained results in this paper is illustrated by numerical examples.     

Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties

This paper investigates the problem of robust ??_∞ static output feedback controller design for a class of discrete‐time piecewise‐affine systems with norm‐bounded time‐varying parametric uncertainties. The objective is to design a piecewise‐linear static output feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop system with a prescribed ??_∞ disturbance attenuation level. Based on a piecewise Lyapunov function combined with S‐procedure, Projection lemma, and some matrix inequality convexifying techniques, several novel approaches to the static output feedback controller analysis and synthesis are developed for the underlying piecewise‐affine systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a family of LMIs parameterized by one or two scalar variables, which are numerically efficient with commercially available software. Finally, three simulation examples are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.     

滞后广义系统的状态反馈H∞控制

研究了一类状态方程和输出方程均带有时滞的滞后广义系统的H_∞控制问题.利用线性矩阵不等式,首先给出滞后广义系统零解渐近稳定且具有H_∞范数约束的充分条件,进而分别设计无记忆和有记忆状态反馈控制律,保证闭环系统具有上述性能,同时基于线性矩阵不等式的解得到了相应控制器构造方法.最后给出一个数值算例说明文中结论的有效性.     

Descriptor discrete-time systems with random abrupt changes: stability and stabilisation

This paper deals with the class of linear discrete-time systems with random abrupt changes also known as class of Markovian jump singular systems. The problems of stochastic stability and the stochastic stabilisation (using state-feedback control and static output feedback control) are tackled. Conditions in the LMI setting to design the appropriate gains of the controllers are developed. It is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities (LMIs) are feasible. Numerical examples are employed to show the usefulness of the proposed results.     

Semi-global sampled-data output feedback disturbance rejection control for a class of uncertain nonlinear systems

This paper investigates the semi-global output feedback disturbance rejection control problem for a class of uncertain nonlinear systems with additive disturbances using linear sampled-data control. Aiming to reject the adverse effects caused by the uncertainties and unknown nonlinear perturbations which may not satisfy the strict feedback or feedforward structure, a new generalised discrete-time extended state observer is proposed to estimate the disturbance at sampling points. An output feedback disturbance rejection control law is then constructed in a sampled-data form which facilitates digital implementations. By selecting adequate control gains and a sufficiently small sampling period to restrain the state growth under a zero-order-hold input, the semi-global asymptotic stability of the hybrid closed-loop system and the disturbance rejection ability are proved. Both numerical example and an application of a single-link robot arm system demonstrate the feasibility and efficacy of the proposed method.     

广义离散系统的状态反馈鲁棒H∞控制及仿真

针对一类范数有界参数不确定性的广义离散线性系统,研究了该系统的状态反馈鲁棒H∞控制问题.利用线性矩阵不等式(LMI)的方法,得到了问题可解的条件,并给出了相应的状态反馈控制律.在一定条件下,所得的状态反馈鲁棒H∞控制律使广义离散线性系统对所有容许的不确定性参数,能够保证闭环系统正则、具有因果关系并且渐进稳定,同时其传递函数矩阵能够满足给定的H∞性能指标.正常离散线性系统的相对应结果可作为论文结果的特殊形式.仿真例子验证了该方法的正确性.     

一类切换线性奇异系统的H∞控制

研究一类由任意有限多个奇异子系统组成的切换奇异系统的状态反馈和动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换策略.分别采用矩阵变换和消元法,将矩阵不等式分别转化为一组线性矩阵不等式(LMIs).数值算例说明了所提方法的有效性和可行性.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> static output feedback control of discrete-time switched polytopic linear systems with average dwell-time

This paper investigates the problem of robust exponential H _∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H _∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler’s lemma and Dualization lemma, some novel conditions for exponential H _∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.     

Static output feedback control for stochastic hybrid systems: LMI approach

This paper deals with the stabilization problem of the class of uncertain stochastic hybrid systems. The uncertainties are norm bounded type. Under the complete access to the system mode a static output feedback controller that makes the closed-loop dynamics of this class of systems regular, impulse-free and stochastically stable is designed. The gains of this controller are the solution of some linear matrix inequalities (LMIs).     

An efficient LMI approach for the quadratic stabilisation of a class of linear,uncertain, time-varying systems

The purpose of this article is to provide a numerically efficient method for the quadratic stabilisation of a class of linear, discrete-time, uncertain, time-varying systems. The considered class of systems is characterised by an interval time-varying (ITV) matrix and constant sensor and actuator matrices. It is required to find a linear time-invariant (LTI) static output feedback controller yielding a quadratically stable closed-loop system independently of the parameter variation rate. The solvability conditions are stated in terms of linear matrix inequalities (LMIs). The set of LMIs includes the stability conditions for the feedback connection of a unique suitably defined extreme plant with an LTI output controller and the positivity of a closed-loop extremal matrix. A consequent noticeable feature of the article is that the total number of LMIs is independent of the number of uncertain parameters. This greatly enhances the numerical efficiency of the design procedure.     

Finite-time control of discrete-time linear systems: Analysis and design conditions

In this paper we deal with some finite-time control problems for discrete-time, time-varying linear systems. First we provide necessary and sufficient conditions for finite-time stability; these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference Lyapunov inequality. Then we address the design problem. The proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite-time sense; all these conditions can be expressed in terms of LMIs and therefore are numerically tractable, as shown in the example included in the paper.     

线性离散时滞系统的输出反馈耗散控制

考虑线性离散时滞系统的二次型耗散控制问题,设计动态输出反馈使闭环系统渐近稳定且严格二次型耗散.先将系统严格二次型耗散性转化为线性矩阵不等式的可解性,得到了系统渐近稳定且严格二次型耗散的条件.然后讨论输出反馈耗散控制问题,给出了控制器的存在条件,总结出了控制器的综合方法、步骤.所得结果可为离散时滞系统的无源控制和H∞控制提供统一框架,也为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

具有外部扰动的离散广义系统有限时间控制

讨论一类具有有限能量的外部扰动的线性离散广义系统的有限时间控制问题。分析问题可解性,得到该问题可解的充分条件,通过状态反馈控制器和输出反馈控制器的设计,给出实现闭环系统有限时间有界的充分条件,这些充分条件可以转化为线性矩阵不等式(LMI)的可行解问题,可借助Matlab中的LMI工具箱求解,最后通过数值算例验证该方法的...     

Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

This paper investigates the problem of simultaneous robust normalization and delay‐dependent H_∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H_∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H_∞ controller alone or a state‐derivative feedback H_∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

线性广义系统的鲁棒严格耗散控制

利用线性矩阵不等式(LMI)方法,给出线性广义系统容许且严格耗散的充分必要条件,由此得到状态反馈和动态输出反馈严格耗散控制器的存在条件及设计方法.考虑除E外所有系数矩阵均具有范数有界时变不确定性的广义系统的鲁棒严格耗散控制问题,给出了系统广义二次稳定且严格耗散的充分条件,以及状态反馈和动态输出反馈鲁棒严格耗散控制器的存在条件及构造方法.