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.     

Non-fragile guaranteed cost control for discrete-time uncertain linear systems

This paper studies the problem of non-fragile guaranteed cost control (GCC) state-feedback design for discrete-time uncertain linear systems. The systems are assumed to have norm-bounded system uncertainties in both the state and the input matrices. The state-feedback gains are assumed to have norm-bounded controller uncertainties which can be either additive or multiplicative. The non-fragile GCC state-feedback designs, which are related to solutions of some matrix inequalities, guarantee the cost of the system to be within a certain bound for all these admissible uncertainties. Our proposed design approach of separating the controller uncertainty from the system uncertainty gives a less conservative solution. A numerical example is given to illustrate the design methods and the design benefits.     

参数不确定广义大系统的保性能分散控制

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.     

Guaranteed Cost Control for Discrete-time Singular Large-scale Systems with Parameter Uncertainty

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper.The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model.The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncer- tainties.A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities(LMIs),and a desired state feedback controller is obtained via con- vex optimization.An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

参数不确定离散广义大系统的保性能控制

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper. The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities (LMIs), and a desired state feedback controller is obtained via convex optimization. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

不确定线性系统保代价控制的鲁棒性分析

研究不确定线性系统保代价控制的鲁棒性分析问题.提出了不确定线性系统保代价 控制鲁棒界概念,给出了不确定线性系统保代价控制的一种鲁棒性分析方法,并建立了不确 定线性系统的参数可变保代价控制鲁棒界.针对一类结构不确定线性系统,进一步给出了保 代价控制鲁棒界的一种优化算法,并用实例加以验证.     

Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback

This paper proposes a systematic approach for the static output feedback control design for discrete-time uncertain linear systems. It is shown that if the open-loop system satisfies some particular structural conditions and the uncertainty has a specific structure, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and nonsquare systems are considered. The performance problem through a quadratic criterion is also discussed (guaranteed cost control).     

Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections

In this paper, the robust non-fragile guaranteed cost-control problem is studied for a class of uncertain linear large-scale systems with time-delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control law such that the closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.     

Quadratic guaranteed cost control for uncertain dissipative models: A Riccati equation approach

The problem of H₂ guaranteed cost control and dynamic output-feedback for linear uncertain systems with dissipative uncertainty is addressed. The problem of robust H₂ synthesis has been open for the last two decades. In this paper, a problem of H₂ quadratic guaranteed cost control is defined for uncertain systems affected by LTI quadratic dissipative model uncertainty. A necessary and sufficient condition of quadratic stabilizability via output-feedback is derived in terms of two coupled parameter-dependent Riccati equations. Then, a method is given to design controllers which minimize an upper bound for the worst-case H₂ norm of the uncertain system. It therefore assesses a guaranteed level of robust performance where in literature, only nominal performance is ensured in most cases. A reliable numerical iterative procedure based on Riccati solvers and one-dimensional convex parameter search is provided. With this uncertainty modelling and the developed numerical procedure, we hope to reduce the usual conservatism of quadratic designs.     

不确定线性时滞系统的一种混杂状态反馈保成本控制及优化设计方法

本文研究一类不确定线性时滞系统的混杂状态反馈保成本控制及优化设计问题.假设存在有限个备选的控制增益已知的控制器,并且其中任何单一的状态反馈控制器都不能镇定系统,基于单Lyapunov函数的方法,给出了混杂状态反馈保成本控制的充分条件及优化设计方案.当备选的控制增益未知时,利用多Lyapunov函数法,同样给出混杂状态反馈保成本控制的充分条件及相应的优化设计方法.最后用仿真验证了文中方法的有效性.     

Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays.

This paper studies the guaranteed cost control problem for a class of uncertain stochastic nonlinear systems with multiple time delays represented by the Takagi-Sugeno fuzzy model with uncertain parameters. By constructing a new stochastic Lyapunov-Krasovskii functional, sufficient conditions for delay-dependent guaranteed cost control are obtained which do not require system transformation or relaxation matrices. Conditions for the existence of an optimal guaranteed cost controller are presented in the linear matrix inequality format. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper.     

Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach

A method is presented for designing a full state feedback linear control law that will ensure the robust stability and performance of a given linear uncertain system. The systems under consideration are described by state equations that depend on uncertain parameters. These uncertain parameters may be time varying. Their values are constrained to lie within known compact bounding sets. The method is based on the guaranteed cost control concept of Chang and Peng (1972). The controller gains result from the solution of a Riccati equation in which the weighting matrices depend on the uncertainty bounds. Sufficient conditions for the existence of a solution arise from the standard LQG control theory.     

不确定系统的网络化保性能控制

本文针对控制网络中存在着随机传输时延和数据包丢失的现象,考虑了网络化控制系统的状态反馈保性能控制器设计问题.首先采用时滞相关方法并引入自由权矩阵,给出了基于矩阵不等式的网络化二次型保性能控制器存在的充分条件,然后基于该充分条件获得了基于线性矩阵不等式的控制器设计方法,相应的网络化保性能控制律可以通过求解线性矩阵不等式来构造,并采用锥互补线性化算法给出了网络化次优保性能控制器的设计方法.最后数值示例演示了所得控制器设计结果的应用方法和有效性,并通过仿真比较了传统保性能控制器和网络化保性能控制器在网络化控制系统中的控制性能.     

Guaranteed cost repetitive control for uncertain discrete-time systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method for the repetitive control systems by introducing a robust output feedback controller so that the closed-loop system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. Necessary and sufficient conditions for the existence of such controllers are derived in terms of linear matrix inequality (LMI). A suboptimal guaranteed cost controller is obtained by solving an optimization problem with LMI constraints. Finally, a simulation example is provided to illustrate the validity of the proposed method.     

Linear quadratic networked control of uncertain polytopic systems

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous‐time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete‐time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete‐time domain assures a guaranteed quadratic cost to the closed‐loop continuous‐time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete‐time domain, a digital robust state feedback control law that stabilizes the original continuous‐time system assuring an upper bound to the quadratic cost of the closed‐loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

一类Delta算子不确定时滞系统保性能滤波

针对一类具有凸多面体参数不确定性的Delta算子时滞系统,研究其保性能滤波问题．采用线性矩阵不等式（LMI）方法,给出了滤波器存在的充分条件和显式表达式．给出的滤波器满足滤波误差动态渐近稳定和保性能方程最小．所提出的方法可将连续系统和离散系统统一到Delta算子框架下．仿真例子证明了该方法的可行性．     

Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay

This paper is concerned with the problem of robust finite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay. Firstly, the definitions of finite-time boundedness, finite-time stabilization, and robust finite-time guaranteed cost control are presented. Next, based on the average dwell-time approach, sufficient conditions on robust finite-time guaranteed cost control are obtained for the uncertain impulsive switched systems. Then, by using multiple Lyapunov-like functional method and linear matrix equality (LMI) technique, the state feedback controller is designed to guarantee that the uncertain impulsive switched system is finite-time stabilized. Furthermore, a finite-time guaranteed cost bound is given. Finally, a numerical example is shown to illustrate the effectiveness of the proposed results.     

Robust Control System Design for an Uncertain Nonlinear System Using Minimax LQG Design Method

A systematic approach to design a nonlinear controller using minimax linear quadratic Gaussian regulator (LQG) control is proposed for a class of multi‐input multi‐output nonlinear uncertain systems. In this approach, a robust feedback linearization method and a notion of uncertain diffeomorphism are used to obtain an uncertain linearized model for the corresponding uncertain nonlinear system. A robust minimax LQG controller is then proposed for reference command tracking and stabilization of the nonlinear system in the presence of uncertain parameters. The uncertainties are assumed to satisfy a certain integral quadratic constraint condition. In this method, conventional feedback linearization is used to cancel nominal nonlinear terms and the uncertain nonlinear terms are linearized in a robust way. To demonstrate the effectiveness of the proposed approach, a minimax LQG‐based robust controller is designed for a nonlinear uncertain model of an air‐breathing hypersonic flight vehicle (AHFV) with flexibility and input coupling. Here, the problem of constructing a guaranteed cost controller which minimizes a guaranteed cost bound has been considered and the tracking of velocity and altitude is achieved under inertial and aerodynamic uncertainties.