【作者】 高鹏；

【导师】 马树萍；

【作者基本信息】 山东大学 ， 运筹学与控制论， 2007， 硕士

【摘要】 本文研究了不确定离散奇异时滞系统的时滞相关型状态反馈保性能控制器的设计问题。考虑不确定离散奇异时滞系统式中x（k）∈Rⁿ是状态变量，u（k）∈R^m是控制输入，E，A，A_d，B为已知适维常矩阵，0＜rankE=r＜n，d是未知的常整数时滞，0＜d≤d_m，d_m为d的上界，d_m是已知的正整数，φ（k）为满足相容性条件的初始函数。ΔA，ΔA_d和ΔB是系统的不确定矩阵并假定有如下形式：[ΔAΔA_dΔB]=MF（k）[N_a N_d N_b] （2）式中M，N_a，N_d和N_b是常数矩阵，F（·）∈R^i×j是未知矩阵并满足F^T（k）F（k）≤I，（?）k. （3）对于给定的对称正定矩阵R₁，R₂，系统（1）的性能指标为本文的目的是设计状态反馈控制器u（k）=Kx（k），K∈R^m×n使得闭环系统正则，因果且渐近稳定，并且使性能指标J满足一个上界。首先，在一般的秩条件下，利用奇异系统的受限等价变换和状态-控制对的线性变换，将系统（1）变成正常的线性离散时滞系统，同时将指标（4）也化成对应的形式。从而将此问题转化成讨论正常离散时滞系统的保性能控制问题。第二节叙述了这一过程。第三节是本文的主要工作，通过引入Lyapunov-Krasovskii泛函，并利用Lyapunov稳定性理论给出了时滞相关型状态反馈保性能鲁棒控制器存在的充分条件，即文中的定理1。为了便于运用Matlab软件包求解，本文将定理1中的矩阵不等式变换成线性矩阵不等式，并给出了控制器的设计方法和性能指标上界。定理2及其证明叙述了这一过程。第四节的数值算例指出了所给出的保性能鲁棒控制器设计方法的有效性。更多还原

【Abstract】 This paper considers the problem of state feedback guaranteed cost controller design for discrete-time singular time-delay systems with norm-bounded parameter uncertainties. Consider uncertain discrete singular time-delay systemswhere x（k） ∈ Rⁿ is the state vector, u（k） ∈ R^m is the controlled input, E, A, A_d, B are unknown real constant matrices with appropriate dimensions, 0 < rankE = r < n, d is an unknown real constant delay and satisfies 0 < d ≤ d_m, where d_m is the upper bound of d. φ（k） is a compatible initial function. ΔA, ΔA_d and ΔB are unknown matrices representing time-varying parameter uncertainties, and assumed to be of the formwhere M,N_a,N_d and N_b, are known real constant matrices, F（·） ∈ R^i×j is an unknown time-varying matrix function satisfyingGiven positive definite symmetric matrices R₁,R₂, we consider the cost functionalThe purpose of this paper is to design a state feedback controller K is a constant matrix, such that for all admissible uncertainties, the closed-loop system is regular, casual and asymptotically stable and the closed-loop value of the cost functional J satisfies a bound.At first, it is assumed that 0 < rankE = r < n. Based on the restricted system equivalent （r.s.e.） transformation and state-controlled input linear transformation, the system（1） is transformed into a linear standard discrete time-delay system, while the cost （4） is also transformed into the corresponding form. Hence we can discuss the problem of guaranteed cost control for linear standard discrete time-delay system instead of that for system （1）. Section two gives this process.Section three is the main work of this paper. By quoting a Lyapunov-Krasovskii function, we establish a delay-dependent sufficient condition for the existence of the state feedback guaranteed cost controller from the Lyapunov stability theory, i.e. Theorem 1. In addition, in order to solve the problem by using the Matlab toolbox, we translate the matrix inequalities of Theorem 1 into the terms of linear matrix inequalities, and then give the design method of the controller in Theorem 2.At last, we illustrate the validity of the result provided in this paper with a numerical example.更多还原