不确定离散时滞模糊系统的保性能控制

针对一类模糊模型表示的，具有范数有界时变参数不确定性离散时滞系统，研究了保性能控制器设计问题。首先推导了保性能控制器存在的充分条件，在此基础上通过求解等价的线性矩阵不等式给出了控制器的设计方法和参数表示。     

不确定线性系统的最优保性能可靠控制

针对一类不确定线性系统,采用连续增益故障模型提出了考虑执行器故障的保性能可靠控制问题.通过对具有执行器增益故障的系统分析,利用线性矩阵不等式(LMI)分别给出了保性能标准控制、最优保性能标准控制、保性能可靠控制、最优保性能可靠控制存在的充分条件.根据凸优化理论,最优保性能标准控制和最优保性能可靠控制的设计方法转化为一个线性凸优化算法.仿真数例验证了文中所提出方法的可行性.在相同形式的故障发生时,比较最优保性能标准控制与最优保性能可靠控制,进一步说明了最优保性能可靠控制的必要性.     

一类具有时变时滞和Markov跳变参数的不确定系统滑模控制

针对一类具有时变时滞和Markov跳变参数的不确定系统,研究基于滑模超平面的变结构控制算法.该算法通过坐标变换将系统描述成简约型,在考虑时变时滞和不确定性的前提下,基于线性矩阵不等式(LMIs)方法给出了滑模平面的设计方法,推导出了随机稳定滑模面存在的充分条件,同时利用指数趋近律构造了整个系统的滑模变结构控制算法,并证明了该算法能够确保系统的运动轨迹在有限时间内到达并一直保持在滑模面上.最后通过数值仿真算例验证了设计方法的正确性和有效性.     

基于T-S模型的不确定时滞系统的保代价控制

基于T—S模糊模型，研究具有范数有界、时变参数不确定性和时滞的非线性系统的保代价控制问题，得到存在稳定模糊保代价控制器的充分条件，并推算出相应的线性矩阵不等式(LMI)形式。     

一类具有饱和因子的奇异时滞系统的鲁棒保性能控制

研究了具有饱和因子的非线性奇异时滞系统的鲁棒保性能控制问题.目的是设计一个鲁棒控制器和保成本控制器,通过线性矩阵不等式方法(LMI)得出了鲁棒控制器和保性能控制器存在的充分条件.当这些LMI方法是可解时,分别给出了鲁棒控制器和保性能控制器的解析表达式.     

变时滞不确定线性系统的H∞控制

对于一类不确定状态时变时滞系统,利用基于时滞划分的Lyapunov-Krasovskii泛函讨论其稳定性,并得到以LMI形式给出的一种保守性小的稳定性条件,最后通过分析并给出了保证系统鲁棒稳定的H∞控制器,数值实例表明了方法的有效性.     

模糊不确定时滞系统的保成本控制

讨论了基于T-S模型的不确定时滞系统的保成本控制问题.文章采用并行补偿状态反馈控制方法和时滞相关稳定性分析方法,通过引入一个带调节因子的Lyapunov-Krasovskii泛函,利用线性矩阵不等式的形式给出了状态反馈控制器存在的充分条件.当调节因子取不同值时,最小保成本值和反馈增益也是不同的,不同的反馈增益导致不同的动态性能,因此,可以通过选取合适的调节因子来优化闭环系统的动态性能. 最小保成本值可以看作调节因子的函数,因此,可以通过求解一个凸优化问题来求得最小的保成本值和最优的调节因子,文章给出了一个求解最小保成本值的算法.并利用仿真示例验证了所给方法的有效性.     

一类不确定区间时变时滞系统的时滞相关鲁棒H_∞控制

研究了一类不确定区间时变状态时滞系统的鲁棒H_∞控制问题.基于Lyapunov稳定性理论和线性矩阵不等式,采用自由权矩阵方法,得到使得相应闭环系统渐近稳定且具有H_∞性能的时滞相关充分条件,并给出状态反馈鲁棒H_∞控制律的设计方法.仿真实例表明了该方法的有效性.     

随机线性系统保成本控制的线性矩阵不等式方法

考虑具有二次成本函数的随机线性系统,研究了状态反馈控制的保证成本控制问题.依据线性矩阵不等式得到了保证成本控制器存在的充分条件,最后得到了随机线性闭环系统保证成本最小的最优保证成本控制律的表达式.     

变时滞不确定线性系统的H_\infty控制

对于一类不确定状态时变时滞系统,利用基于时滞划分的Lyapunov-Krasovskii泛函讨论其稳定性,并得到以LMI形式给出的一种保守性小的稳定性条件,最后通过分析并给出了保证系统鲁棒稳定的H_\infty控制器,数值实例表明了方法的有效性.     

Robust guaranteed cost control for uncertain linear differential systems of neutral type

In this paper, the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated. The uncertainty is assumed to be norm-bounded and time-varying nonlinear. The problem is to design a state feedback control laws such that the closed-loop system is robustly stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay. A criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the Lyapunov method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.     

Output-feedback guaranteed cost control for uncertain time-delay systems with Markov jumps

This paper considers the guaranteed cost control problem ofthe jump linear system with uncertain parameters and constanttime delay. The sufficient and necessary condition for the systemto be mean square quadratically stable (MSQS) is obtained. Usingthe LMI technique, an algorithm to design an output-feedbackguaranteed controller which stabilizes the system in the MSQSsense is developed.     

Constrained control for uncertain linear systems

The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.The author is grateful to Drs. Vito Cerone and Roberto Tempo for their comments.     

On the robustness of linear stabilizing feedback control for linear uncertain systems

We investigate linear time-invariant scalar-input systems with constant uncertainties that are not required to satisfy matching conditions. In a previous paper, the existence of stabilizing discontinuous controllers is established under three assumptions for such systems. The first assumption requires controllability of the system for each uncertainty. The second is a condition on an uncertain Lyapunov equation, and the third is a boundedness condition related to the controllability matrix. In this paper, using the same assumptions, we show the existence of a linear stabilizing control. Our result is related to the high-gain theorem of classical control.     

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless 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. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.     

Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

Email: chlien{at}mail.nkmu.edu.tw Received on August 10, 2006; Accepted on September 6, 2006 In this paper, delay-dependent guaranteed cost observer-basedcontrol for neutral systems with time-varying delays is considered.Control and observer gains will be given from the linear matrixinequality feasible solutions. Optimal guaranteed cost observer-basedcontrol which will minimize the guaranteed cost of the systemis provided.     

Robust guaranteed cost control for discrete‐time systems via partially delay‐dependent controller with linear fractional uncertainties

In this article, a partially delay‐dependent controller is designed to analyze the guaranteed performance analysis of a class of uncertain discrete‐time systems with time‐varying delays. By constructing suitable Lyapunov–Krasovskii Functional (LKF), sufficient conditions are derived to ensure the system to be robustly stochastically stable in mean square sense by using Wirtinger‐based inequality and convex reciprocal lemma. The proper cost function is chosen to guarantee an adequate level of performance. The derived conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in MATLAB. Further, the advantage of employing the obtained results is illustrated via numerical examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 113–122, 2016     

On the robustness of linear stabilizing feedback control for linear uncertain systems: Multi-input case

The robust stabilization of linear systems with constant uncertainties against structured perturbations using Lyapunov's theory is investigated. The only information needed on the uncertainties is the knowledge of their boundaries. The matching conditions of the uncertain systems are not required to be satisfied. It is first shown that, under some assumptions, the system can be transformed into a certain canonical controllable companion form. Then, under some additional assumptions, the existence of a linear controller which stabilizes the system based on Lyapunov's theory is shown.     

On guaranteed stability of uncertain linear systems via linear control

This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix (q) (formed using the given data) is negative definite for allq Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390.     

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be possibly fast, time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the original uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball of the original system can be made arbitrarily small by suitable choice of design parameters.