离散非线性时变凸多面体系统族的鲁棒正不变集  

ROBUST POSITIVELY INVARIANT SETS OF DISCRETE TIME NONLINEAR AND TIME VARIABLE CONVEX POLYHEDRAL SYSTEM FAMILY

作　　者：蒋卫华[1] 黄琳[2] 楚天广[2] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001 [2]北京大学力学与工程科学系,北京100871

出　　处：《自动化学报》2001年第5期631-636,共6页Acta Automatica Sinica

基　　金：国家自然科学基金 ( 1 9872 0 0 5 );哈尔滨工业大学学校基金;国家攀登计划资助

摘　　要：动态系统的状态约束和控制约束等问题可归结为状态空间中某些集合的正不变性 .利用混合单调分解方法研究离散非线性、时变凸多面体系统族的线性状态约束集合的鲁棒正不变性 .对由矩阵凸多面体和加性区间扰动描述的线性时变离散系统族 ,得到了鲁棒正不变集的充分必要条件 ;对非线性系统族则得到有关充分条件 .这些条件均由系统族的顶点表述 ,易于检验 .同时给出示例 .Certain problems concerning state constraints and control constraint can often be reduced to the study of positive invariance of some subsets of the state space of dynamical systems. The robust positive invariance of given linear state constraint sets of uncertain discrete-time systems is studied by means of the mixed monotone decomposition method. Necessary and sufficient conditions of the robust positively invariant sets are established for the linear discrete-time system family specified by matrix convex polyhedron and additive interval disturbances. Also, sufficient conditions are derived for nonlinear system family. All the conditions are given in terms of the parameters of vertex systems of the system family and are therefore easy to check. Finally, an illustrating example is given.

关 键 词：离散系统族 鲁棒正不变集 混合单调分解方法 顶点检验 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]