Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ?₂-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.     

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.     

Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ?_∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ?₂ (?₂)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.     

Output feedback control for uncertain linear systems with faulty actuators based on a switching method

This paper investigates the problem of output feedback stabilization for a class of uncertain linear systems with faulty actuators via the synergy with a switching strategy. When actuators suffer a ‘destabilizing failure’ and the never‐faulty actuators cannot stabilize the given system, the closed‐loop exponential stability can still be achieved via the average dwell‐time scheme employing an arbitrary switching signal. The prerequisite condition found requires the ratio between the two lapse times, when the system is devoid of faulty actuators and when it is not so, to be less than a certain specified constant. Then the stabilizing output feedback controls are designed via the technique of linear matrix inequalities. The illustrative example and the respective simulation results demonstrate the feasibility and effectiveness of the proposed design synthesis. Copyright © 2008 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.     

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.     

Output tracking control for networked control systems with time delay and packet dropout

This article studies the problems of H _∞ output tracking performance analysis and controller design for networked control systems (NCSs) with time delay and packet dropout. By using linear matrix inequality (LMI)-based method, H _∞ output tracking performance analysis and controller design are presented for NCSs with constant sampling period. For NCSs with time-varying sampling period, a multi-objective optimisation methodology in terms of LMIs is used to deal with H _∞ output tracking performance analysis and controller design. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The simulation results illustrate the effectiveness of the proposed H _∞ output tracking controller design.     

线性切换容错控制系统稳定性的新判据*

研究了线性切换容错控制系统的稳定性问题。利用分段李雅普诺夫函数方法,结合梅茨勒矩阵的性质和矩阵不等式的分析技巧,得到了基于李雅普诺夫—梅兹勒线性矩阵不等式判定系统稳定的新结果。设计依赖于状态的切换规则便于计算、易于检验。最后利用MATLAB工具箱得到的仿真实例验证了本结果的可行性。     

Linear matrix inequalities for analysis and control of linear vector second‐order systems

Many dynamical systems are modeled as vector second‐order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second‐order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter‐dependent Lyapunov functions as certificates of stability of uncertain and time‐varying vector second‐order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second‐order form. Copyright © 2014 John Wiley & Sons, Ltd.     

Uniform stabilization of discrete-time switched and Markovian jump linear systems

The uniform stability of discrete-time switched linear systems, possibly with a strongly connected switching path constraint, and the existence of finite-path-dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite-dimensional feasible system of linear matrix inequalities. This characterization is based on the observation that a linear time-varying system is uniformly stable only if there exists a finite-path-dependent quadratic Lyapunov function. The synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities. The result carries over to the almost sure uniform stabilization of Markovian jump linear systems.     

Static output feedback control design for linear MIMO systems with actuator dynamics governed by diffusion PDEs

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.     

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.     

Stabilization of linear systems with time‐varying delays

This paper is concerned with the stability and stabilization problems for a class of time‐delayed systems, whose time‐varying delays are studied via Markovian approach. By separating the delay interval into several subintervals and by considering the inherent distribution of time‐varying delay, a new model is firstly developed. On the basis of the established model, a novel Lyapunov functional, which makes full use of each subinterval's delay bounds and the randomicity of time‐varying delay, is constructed to drive less conservative stability criteria. Especially sufficient conditions for the existence of stabilizing controllers are obtained as linear matrix inequalities, which are further used to deal with networked control systems. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.     

Delay‐dependent adaptive reliable H∞ control of linear time‐varying delay systems

This paper considers the problem of delay‐dependent adaptive reliable H_∞ controller design against actuator faults for linear time‐varying delay systems. Based on the online estimation of eventual faults, the parameters of adaptive reliable H_∞ controller are updating automatically to compensate the fault effects on the system. A new delay‐dependent reliable H_∞ controller is established using a linear matrix inequality technique and an adaptive method, which guarantees the stability and adaptive H_∞ performance of closed‐loop systems in normal and faulty cases. A numerical example and its simulation results illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Quadratic stabilizability and H∞ control of linear discrete‐time stochastic uncertain systems

This paper considers quadratic stabilizability and H_∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l²‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.     

An Alternative approach to H∞ control for fuzzy systems

In this paper the problem of H_∞ dynamic feedback control for fuzzy dynamic systems has been studied. First the problem of H_∞ dynamic feedback controller designs for complex nonlinear systems, which can be represented by Takagi‐Sugeno (T‐S) fuzzy systems, is presented. Second, based on a Lyapunov function, four new dynamic feedback H_∞ fuzzy controllers are developed by adequately considering the interactions among all fuzzy sub‐systems and these dynamic feedback H_∞ controllers can be obtained by solving a set of suitable linear matrix inequalities. Finally, two examples are given to demonstrate the effectiveness of the proposed design methods. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Multi‐objective state feedback control for linear delay systems

This paper provides new linear matrix inequalities (LMI)‐based formulae for mixed H₂/H_∞ state‐feedback synthesis of linear continuous‐time systems with state delays of any size. The proposed delay‐independent LMI‐based conditions enable us to parameterize a memoryless state‐feedback controller without involving the Lyapunov variables in the formula. Compared with previous results based on a common Lyapunov variable, the proposed formula provides less conservative results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society