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.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY

This paper deals with the problem of stability and robust control for both certain and uncertain continuous‐time singular systems with state delay. Systems with norm‐bounded parameter uncertainties are considered. Robust delay‐dependent stability criteria and linear memoryless state feedback controllers based on linear matrix inequality are obtained. By choosing some Lyapunov‐Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay‐dependent results. Finally, numerical example is provided to illustrate the effectiveness of the proposed method.     

Event‐triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。     

不确定性关联时滞大系统的分散鲁棒控制——LMI方法

对一类满足匹配条件的不确定性关联时滞大系统,Lyapunov稳定性原理,给出了其可分散状态反镇定的充分条件,即一组线性矩阵不等式（LMI）有解,在此基础上,通过求解一凸优化问题,提出了具有较小的反馈增益的分散稳定化状态反馈控制律的设计方法,文中最后用示例说明了该方法的应用与优越性。     

Robust model predictive control of a class of uncertain nonlinear systems with application to typical CSTR problems

This paper proposes a robust predictive control approach for additive discrete time uncertain nonlinear systems. The controller design is characterized as an optimization problem of the “worst-case” objective function over an infinite moving horizon. A sufficient state feedback synthesis condition is provided in the form of a linear matrix inequality (LMI) optimization and is solved online at each time step. A few simulation examples are exploited to illustrate the effectiveness of this method. Among them are two typical CSTR problems.     

含状态时滞及执行器饱和不确定系统反馈镇定及L2增益分析

研究了具有控制饱和状态时滞不确定系统的L2控制问题,提出了状态反馈方法,利用Lyapunov函数可获得时滞相关的线性矩阵不等式.线性矩阵不等式条件可保证闭环系统无干扰时鲁棒内稳定性和在某椭球内预先给定的有干扰时L2性能水平,该不等式通过引入辅助矩阵解除了执行器饱和对系统的影响而更易于实现且减小了保守性.采用线性矩阵不等式技术,将控制器存在的充分条件转化为凸优化问题.在此基础上设计了系统的状态反馈控制器,最后用数值仿真验证了所提出方法的可行性.     

时变不确定性关联系统的分散鲁棒稳定控制器设计

对一类满足匹配条件的时变不确定性关联大系统,给出了其可分散状态反馈镇定的充分条件即一组线性矩不等式（ＬＭＩ）有解,在此基础上,通过求解一凸优化问题,指出了具有较小反馈益的分散稳定化状态反馈控制律的设计方法,文中的仿真示例说明了该方法的有铲笥和优越性。     

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.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.     

结构不确定离散系统的最优非脆弱保成本控制

讨论了一类不确定线性离散系统的最优非脆弱保成本控制问题.考虑的系统和状态反馈控制器均具有时变的结构化的不确定性.基于线性矩阵不等式的方法,给出了存在和设计非脆弱保成本控制律的一个充分条件,以及在使二次成本函数上界最小意义下,最优非脆弱保成本控制律的凸优化设计方法.并用数值例子说明该方法降低了成本函数上界的保守性.     

时延不确定离散时间系统的鲁棒跟踪控制

研究一类时延不确定离散时间系统的鲁棒跟踪控制问题．基于线性矩阵不等式(LMI)的控制方法，设计无记忆反馈控制器，构造了适用于时延不确定离散时间系统的Lyapunov函数．通过求解一个LMI便可得到控制器的增益矩阵，从而使系统的状态变量渐近跟踪预先设定的轨迹．仿真示例说明所提出的鲁棒跟踪控制算法是有效的．     

线性离散时滞系统鲁棒严格耗散控制

提出线性离散时滞系统的耗散控制问题,研究无记忆状态反馈控制律存在的条件及 相应的控制器设计方法,以使相应的闭环系统渐近稳定,同时具有严格(Q,S,R)-耗散性.进 一步考虑耗散的不确定性,研究不确定系统鲁棒严格耗散控制的分析与综合问题.结果表明, 鲁棒耗散控制器存在的条件和综合问题等价于线性矩阵不等式(LMI)的可解性问题.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE‐TIME SINGULAR SYSTEMS WITH TIME‐DELAY AND NONLINEAR PERTURBATION

This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.     

带饱和执行器的不确定时滞系统的 鲁棒控制

研究了一类具有饱和执行器约束的不确定时滞系统时滞依赖型无记忆鲁棒控制问题 .所考虑的时滞系统包括时变未知但有界的不确定参数以及状态和控制的时滞项 .文中应用了 Lyapunov定理以及线性矩阵不等式 ( LMI)方法来研究该系统的分析和综合问题 ,导出了一个新的鲁棒可镇定判据和相应的无记忆鲁棒镇定控制律设计方法 .所得的基于一组LMIs的结果是与时滞相关的     

AN LMI APPROACH TO ROBUST STABILITY OF UNCERTAIN DISCRETE SINGULAR TIME‐DELAY SYSTEMS

The problem of robust stability analysis for uncertain discrete singular time‐delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time‐delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncertain discrete singular time‐delay system. Two numerical examples are provided to demonstrate the feasibility of the proposed approach.     

Robust State Feedback Formulation for High Order Repetitive Controllers

This paper presents a robust state feedback formulation for high order repetitive controllers (HORC) able to track references and/or reject disturbances with uncertain period. We propose a modified structure of the HORC with low‐pass filter in series with the delay element, allowing us to work in the state‐space framework. The filter cut‐off frequency effects and the controller sensitiveness to harmonic and intermediary components are analyzed. A methodology based on the solution of an optimization problem subject to linear matrix inequality constraints is presented for robust synthesis of feedback gains. The advantages regarding the proposed control scheme are discussed with a simulated example of a DC motor driving an eccentric mass.