Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.     

Guaranteed cost control for saturated uncertain linear systems

In this paper, we discuss the problem of guaranteed cost control for uncertain linear systems subject to actuator saturation. Based on the quadratic and non-quadratic Lyapunov functions, sufficient conditions for the robust stability and performance are derived. Moreover, all the conditions can be expressed as linear matrix inequalities （LMIs） or bilinear matrix inequalities （BMIs） in terms of the feedback gain. Thus, the static controller can be effectively synthesized via convex optimization. A numerical example illustrates the effectiveness of the method.     

A team algorithm for robust stability analysis and control design of uncertain time‐varying linear systems using piecewise quadratic Lyapunov functions

A team algorithm based on piecewise quadratic simultaneous Lyapunov functions for robust stability analysis and control design of uncertain time‐varying linear systems is introduced. The objective is to use robust stability criteria that are less conservative than the usual quadratic stability criterion. The use of piecewise quadratic Lyapunov functions leads to a non‐convex optimization problem, which is decomposed into a convex subproblem in a selected subset of decision variables, and a lower‐dimensional non‐convex subproblem in the remaining decision variables. A team algorithm that combines genetic algorithms (GA) for the non‐convex subproblem and interior‐point methods for the solution of linear matrix inequalities (LMI), which form the convex subproblem, is proposed. Numerical examples are given, showing the advantages of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.     

On delay‐dependent LMI‐based guaranteed cost control of uncertain neutral systems with discrete and distributed time‐varying delays

In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov–Krasovskii functional theory, a delay‐dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed‐loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd.     

An Lmi Approach To Non‐Fragile Guaranteed Cost Control Of Uncertain Discrete Time‐Delay Systems

This paper studies the non‐fragile Guaranteed Cost Control (GCC) problem via memoryless state‐feedback controllers for a class of uncertain discrete time‐delay linear systems. The systems are assumed to have norm‐bounded, time‐varying parameter uncertainties in the state, delay‐state, input, delay‐input and state‐feedback gain matrices. Existence of the guaranteed cost controllers are related to solutions of some linear matrix inequalities (LMIs). The non‐fragile GCC state‐feedback controllers are designed based on a convex optimization problem with LMI constraints to minimize the guaranteed cost of the resultant closed‐loop systems. Numerical examples are given to illustrate the design methods.     

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.     

An LMI approach to guaranteed cost control for uncertain linear neutral delay systems

This paper considers the problem of guaranteed cost control for uncertain neutral delay systems with a quadratic cost function. The system under consideration is subject to norm‐bounded time‐varying parametric uncertainty appearing in all the matrices of the state‐space model. The problem we address is the design of a state feedback controller such that the closed‐loop system is not only stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is given in terms of a linear matrix inequality (LMI). When this condition is feasible, the desired state feedback controller gain matrices can be obtained via convex optimization. An illustrative example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

不确定离散切换系统具有极点约束的保性能控制

对一类含有范数有界不确定性的离散切换系统和一个二次型性能指标，研究其具有闭环极点约束的鲁棒状态反馈保性能控制问题．利用二次Lyapunov函数方法和线性矩阵不等式技术，给出了鲁棒保性能控制器存在的一个充分条件，在所构造切换规则下，闭环系统二次D稳定，且满足给定的性能指标．在此基础上，将次优保性能控制器设计问题转化为一组线性矩阵不等式约束下的凸优化问题．数值例子说明了所提方法的有效性．     

An LMI approach to output‐feedback‐guaranteed cost control for uncertain time‐delay systems

This paper considers the problem of output‐feedback‐guaranteed cost controller design for uncertain time‐delay systems. The uncertainty in the system is assumed to be norm‐bounded and time‐varying. The time‐delay is allowed to enter the state and the measurement equations. A linear quadratic cost function is considered as a performance measure for the closed‐loop system. Necessary and sufficient conditions are provided for the construction of a guaranteed cost controller. These conditions are given in terms of the feasibility of LMIs which depend on a positive definite matrix and a scaling variable. A numerical algorithm is developed to search for a full order dynamic output‐feedback controller which minimizes the cost bound. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite‐Time Guaranteed Cost Control of Caputo Fractional‐Order Neural Networks

In this paper, we investigate the problem of finite‐time guaranteed cost control of uncertain fractional‐order neural networks. Firstly, a new cost function is defined. Then, by using linear matrix inequalities (LMIs) approach, some new sufficient conditions for the design of a state feedback controller which makes the closed‐loop systems finite‐time stable and guarantees an adequate cost level of performance are derived. These conditions are in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.     

不确定广义系统的保性能控制

针对一类具有范数有界不确定性的连续广义系统和一种具有时间乘积形式的二次性能指标,研究其状态反馈保性能控制器的设计问题.这种性能指标能够使系统状态响应随着时间的增加更快地趋于零,从而缩短系统达到稳定所需要的时间.文中给出了最优保性能控制器存在的充分必要条件并基于双线性矩阵不等式(BMI)、二次矩阵不等式(QMI)和LMI给出其设计方法,最后利用SDP软件和BMI软件举例说明所得结论的可行性.     

时变不确定系统鲁棒控制器设计的新方法

基于包含两个二次项的分段Lyapunov函数,研究了线性时变不确定系统的鲁棒控制器设计问题.所考虑的系统由两个矩阵的凸组合构成,通过引入一个附加矩阵,推导出鲁棒控制器存在的充分条件.该控制器的状态反馈增益的求解问题可以转化为一组带有两个比例参数的线性矩阵不等式的凸优化问题.最后的数值示例说明了该设计方法的可行性.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

A BMI approach for ℋ︁∞ gain scheduling of discrete time‐varying systems

The problem of gain‐scheduled state feedback control for discrete‐time linear systems with time‐varying parameters is considered in this paper. The time‐varying parameters are assumed to belong to the unit simplex and to have bounded rates of variation, which depend on the values of the parameters and can vary from slow to arbitrarily fast. An augmented state vector is defined to take into account possible time‐delayed inputs, allowing a simplified closed‐loop analysis by means of parameter‐dependent Lyapunov functions. A gain‐scheduled state feedback controller that minimizes an upper bound to the ??_∞ performance of the closed‐loop system is proposed. No grids in the parametric space are used. The design conditions are expressed in terms of bilinear matrix inequalities (BMIs) due to the use of extra variables introduced by the Finsler's lemma. By fixing some of the extra variables, the BMIs reduce to a convex optimization problem, providing an alternate semi‐definite programming algorithm to solve the problem. Robust controllers for time‐invariant uncertain parameters, as well as gain‐scheduled controllers for arbitrarily time‐varying parameters, can be obtained as particular cases of the proposed conditions. As illustrated by numerical examples, the extra variables in the BMIs can provide better results in terms of the closed‐loop ??_∞ performance. Copyright © 2009 John Wiley & Sons, Ltd.     

基于LMI 的不确定随机系统输出反馈保性能控制

针对一类不确定连续随机系统,研究了具有输出反馈控制器的保性能控制．首先,对于范数有界 的不确定随机系统,得到了具有输出反馈控制器的闭环系统的二次型性能指标的上界一般形式．其次,应用 线性矩阵不等式技术,研究了其闭环系统的二次稳定和二次保性能稳定;并且依据线性矩阵不等式优化方法, 得到了使闭环系统渐近稳定的最优输出反馈保性能控制器．最后,给出仿真算例,验证本文方法的可行性和 有效性．     

Piecewise Fuzzy Anti-Windup Dynamic Output Feedback Control of Nonlinear Processes With Amplitude and Rate Actuator Saturations

In this paper, a novel anti-windup dynamic output compensator is developed to deal with the robust H _infin output feedback control problem of nonlinear processes with amplitude and rate actuator saturations and external disturbances. Via fuzzy modeling of nonlinear systems, the proposed piecewise fuzzy anti-windup dynamic output feedback controller is designed based on piecewise quadratic Lyapunov functions. It is shown that with sector conditions, robust output feedback stabilization of an input-constrained nonlinear process can be formulated as a convex optimization problem subject to linear matrix inequalities. Simulation study on a strongly nonlinear continuously stirred tank reactor (CSTR) benchmark plant is given to show the performance of the proposed anti-windup dynamic compensator.     

时变不确定多时滞连续系统的最优保成本控制

针对一类同时具有状态多时滞和输入多时滞的时变不确定连续多时滞系统。研究保成本状态反馈控制器的设计。假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件,通过构造改造的Lyapunov函数和线性矩阵不等式（LMI）方法,给出系统满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界。通过求解凸优化问题得到最优保性能控制器,最后用数值例子说明该方法的有效性。     

Robust H∞ Output Tracking Control with Partly Quantized Information

This paper is concerned with the stability and output tracking problems of networked control systems (NCSs) with partly quantized information. Both the remote and local systems are considered. The state variables transported from the remote system experiences time delays and quantization errors, while the local state variables do not. The purpose is to design a state feedback controller which guarantees that the output of the local system tracks the output of the remote system in the H∞ sense. This consideration is widely appeared in remote assistant systems. Based on the Lyapunov–Krasovskii (L‐K) functional approach, sufficient conditions on the existence of a quantized robust H∞ output tracking controller for NCSs are presented in terms of bilinear matrix inequalities (BMIs). Furthermore, a cone complementarity algorithm is used to convert these BMIs into a convex optimization problem. Finally, a simulation example is given to demonstrate the efficiency of the proposed method.     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Fuzzy guaranteed cost control for nonlinear systems with time-varying delay

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.