一类不确定模糊动态时滞系统保成本控制

针对一类不确定非线性动态时滞系统，利用模相T—S模型，通过状态反馈对保成本控制问题进行研究。应用线性矩阵不等式给出模糊闭环系统渐近稳定的充分条件，保证了所有允许的不确定闭环系统是稳定的，而且对于一个给定的二次型成本函数，舱保证闭环成本不超过某个界。仿真结果表明所提出的控制方法是有效的。     

Guaranteed cost control of discrete-time uncertain systems with both state and input delays

The paper proposes a guaranteed cost feedback control for discrete-time uncertain systems with both state and input delays. The delays are assumed to be time-varying and bounded. In addition to norm-bounded parametric uncertainties, the class of admissible uncertainties and nonlinearities of the system comprehend several types of uncertainties frequently investigated in the literature. Using some recent developments, new sufficient conditions for the existence of the guaranteed cost control are given by bilinear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed method.     

Robust nonfragile guaranteed cost control for uncertain T-S fuzzy Markov jump systems with mode-dependent average dwell time and input constraint

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain Takagi-Sugeno fuzzy systems with Markov jump parameters, time-varying delay and input constraint. A nonfragile mode-dependent fuzzy controller with mode-dependent average dwell time (MDADT) is designed with input constraint. A sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.     

一类不确定广义系统的非脆弱保性能控制

研究了一类时变时滞不确定广义系统的非脆弱保性能控制问题。在系统矩阵、滞后状态矩阵、输入矩阵和滞后输入矩阵都具有不确定性时,带有反馈增益扰动的控制器能够保证闭环系统是正则、无脉冲、指数稳定的;且性能函数存在上界。对于出现的两个不确定项乘积的问题,采用两个线性矩阵不等式,两次运用Schur补引理的方法得以解决。控制器的增益可通过求解一系列严格线性矩阵不等式得到。数值仿真实例证明了所提方法的有效性。     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Guaranteed cost output control for uncertain neutral systems with time-varying delays via LMI

In this paper, the robust guaranteed cost output control for a class of uncertain neutral system with time-varying delays is considered. Based on Lyapunov–Krasovskii functional theory, some stabilization criteria are derived and guaranteed costs are given. Delay-dependent and delay-independent criteria are proposed for the stabilization of the system. Static output linear feedback control is considered to stabilize the uncertain neutral system. Linear matrix inequality (LMI) approach and parametrizing transformation approach are used to solve the stabilization problems. A procedure for the controller design is provided. Optimal guaranteed cost output control will be achieved when the optimization problem under LMI conditions can be solved. Finally, two numerical examples are illustrated to show the use of the results.     

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method. Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Young Il Lee. Jong-Hae Kim received the B.S., M.S., and Ph.D. degrees in Electronics from Kyungpook National University in 1993, 1995, and 1998, respectively. He was with STRC at Kyungpook National University from Nov. 1998 to Feb. 2002. He has been with Sun Moon University since March, 2002. His research interests focus on robust control, signal processing, and industrial application systems.     

具有时延和切换拓扑的高阶离散时间多智能体系统鲁棒保性能一致性

研究存在参数不确定性的高阶离散时间多智能体系统在时延和联合连通切换通信拓扑条件下的鲁棒保性能一致性问题,给出一种线性一致性协议的设计方法.1）引入高阶离散时间不确定多智能体系统的鲁棒保性能一致性问题,定义基于智能体邻居状态误差和控制输入的保性能函数;2）通过构造合适的Lyapunov函数并利用离散时间系统稳定性理论,推导出一个使高阶离散时间不确定多智能体系统在该条件下获得保性能一致性的线性矩阵不等式（Linear matrix inequality,LMI）充分条件,并给出相应的保性能上界;3）以一致性序列的形式给出参数不确定条件下的高阶离散时间多智能体系统的一致性收敛结果;4）数值仿真验证了本文理论的正确性和有效性.     

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with timevarying delays are investigated. The idea of guaranteed cost control is introduced into consensus problems for high-dimensional multi-agent systems with time-varying delays, where a cost function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality (LMI), sufficient conditions for guaranteed cost consensus and consensualization are given. Moreover, a guaranteed cost upper bound of the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independent of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.      

基于T-S模型的倒立摆最优保性能模糊控制

对一类具有范数有界参数不确定性T-S模糊模型系统,采用状态反馈的并行分布补偿器(PDC)结构,基于线性矩阵不等式处理方法,研究了其最优保性能模糊控制律的设计问题.导出了保性能模糊控制律存在的条件,通过求解一个凸优化问题给出了最优保性能模糊控制律的设计方法,并用此方法设计了倒立摆系统的最优保性能模糊控制器.仿真实验验证了该设计方法的有效性.     

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.     

不确定随机时滞系统的鲁棒H∞保性能控制

讨论了一类具有时变时滞的不确定It类型随机系统的鲁棒H∞保性能控制问题. 运用Lyapunov-Krasovskii泛函方法, 设计使得闭环系统鲁棒随机指数均方稳定, 且具有给定H∞干扰抑制度 γ 的状态反馈保性能控制器. 控制器存在的充分条件以线性矩阵不等式(LMIs)的形式表示. 进一步, 通过求解具有LMIs约束的凸优化问题, 给出了不确定随机时滞系统的最优保性能控制器的设计方法. 最后通过一个数值例子验证了所提方法的有效性.     

时变不确定切换广义系统的鲁棒最优保性能控制

针对一类时变参数不确定切换广义系统,对其鲁棒最优保性能控制问题进行研究,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。通过构造广义Lyapunov函数和线性矩阵不等式方法,给出系统鲁棒最优保性能控制器存在的充分条件。进一步,建立一个具有线性矩阵不等式约束的凸优化问题,得到鲁棒最优保性能控制律及闭环性能指标上界。最后用示例说明该方法的有效性。     

跳变双线性随机离散组合系统的保成本分散控制

研究一类跳变双线性随机离散组合系统的保成本分散控制问题．首先给出问题可解的充分条件,然后基于线性矩阵不等式方法设计保成本分散状态反馈控制律．理想的保成本分散状态反馈控制器可通过应用现有的软件，求解一组线性矩阵不等式而得到．仿真例子说明了该方法的有效性.     

H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty

This paper presents a design method of H₂ guaranteed cost (GC) fuzzy controllers for discrete-time nonlinear systems with parameter uncertainties. The Takagi and Sugeno (T-S) fuzzy model with parameter uncertainties is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of H₂ GC fuzzy controllers is presented in terms of linear matrix inequalities (LMIs). The resulting fuzzy controllers not only guarantee that the closed-loop fuzzy system is quadratically stable, but also provide a guaranteed cost on the H₂ performance index. Furthermore, an optimal H₂ GC fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an LMI optimization procedure. Finally, it is also demonstrated, through numerical simulations on the backing up control of a truck-trailer, that the proposed design method is effective.     

基于T-S模型的非线性时滞系统非脆弱保性能模糊控制

针对一类用T-S模糊模型描述的非线性时滞系统,采用状态反馈的并行分布补偿方法,研究其保守性较小的非脆弱保性能模糊控制问题,使闭环系统在控制器存在加性摄动的情况下,其闭环性能指标值低于确定的上界.利用线性矩阵不等式处理方法,导出了非脆弱保性能模糊控制律的存在条件,通过建立和求解一个线性矩阵不等式问题,给出了非脆弱保性能模糊控制律的设计方法.仿真结果表明了所提出方法的有效性.     

不确定非线性系统的时滞依赖保性能控制

针对一类基于T-S模糊模型表示的具有时变状态时滞和范数有界不确定性非线性系统，研究了时滞依赖保性能模糊控制器设计问题。对于用T-S模糊模型表示的非线性时滞系统，已知系统的时变时滞本身及其变化率的上界，采用并行分散补偿技术，通过选取合适的Lyapunov函数，推导了依赖时滞上界及变化率上界的时滞保性能模糊控制器存在的充分条件，进而通过建立和求解LMI（线性矩阵不等式）约束的凸优化问题，给出了保性能控制律的设计方法。数值算例表明了该方法的有效性。