不确定离散广义系统的D稳定鲁棒控制  

Robust Control for Uncertain Discrete-Time Singular Systems with D-Stability

作　　者：胡刚[1] 谢湘生[2] 

机构地区：[1]广东工业大学自动化学院,广州510090 [2]广东工业大学系统工程研究所,广州510090

出　　处：《自动化学报》2003年第1期142-148,共7页Acta Automatica Sinica

基　　金：广东省自然科学基金 (0 2 0 16 3)资助~~

摘　　要：研究了具有圆盘区域极点约束的一类不确定离散广义系统的鲁棒控制问题 .首先 ,研究了控制输入项不含扰动的不确定离散广义系统 ,提出了广义二次D镇定的概念 ,基于矩阵不等式和广义Riccati方程 ,给出了一种广义二次D镇定器的设计方法 ,所得到的结论能够实现研究目标 ;然后 ,讨论了控制输入项含有扰动的不确定离散广义系统 ,在一定的假设条件下 ,给出了期望状态反馈增益阵的存在条件及其解析表达式 .最后 ,用数值示例说明所给方法的有效性及可行性 .This paper is concerned with the robust control problems for uncertain discrete-time singular systems with disk pole constraints. First of all, we discuss the uncertain discrete-time singular system without control input matrix perturbation. The concept of generalized quadratic D-stabilizability is put forward for uncertain discrete-time singular systems. A method of designing the state feedback controller is presented based on some matrix inequalities and the generalized Riccati equation, so that the singular closed-loop system is regular, causal, and satisfies that all finite closed-loop poles are located within a pre-assigned circular region for all admissible parameter uncertainties. Secondly, we discuss the uncertain discrete-time singular system with control input matrix perturbation. The condition for the existence of desired robust state feedback gain matrix is obtained; furthermore, the analytical expression of the desired robust state feedback gain matrix is also derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

关 键 词：不确定离散广义系统 D稳定 鲁棒控制 镇定器 RICCATI方程 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]