具有时变参数不确定性线性系统的最优保成本控制

对一类具有块对角参数不确定性的系统，导出了二次保成本状态反馈控制律存在的条件，进而证明了这个条件等价于一组线性矩阵不等式的可解性问题，并通过这组线性矩阵不等式的解，给出了系统二次保成本控制律的一个参数化表示．在此基础上，将最优保成本控制律的设计问题转化成一个凸优化命题，而后者可以用现有的有关线性矩阵不等式软件求解．最后，给出了一个例子，以说明本文提出的方法，并和现有方法作了比较．表1，参10

GUARANTEED COST CONTROL OF LINEAR SYSTEMS WITH TIME-VARYING PARAMETRIC UNCERTAINTY

For a class of systems With block diagonal time - varying parametric uncertainty and a given quadratic cost function, a sufficient condition for the existence of guaranteed cost state feedback control laws is derived, it is shown that this condition is equivalent to the solvability of a system of linear matrix inequalities, and its solutions provide a parametrized representation of the set of guaranteed cest control laws. Based on this fact, the problem of designing an optimul guaranteed cost control law is formulated as a convex programme with linear matrix inequality constraints, which can be solved by using the existing efficient convex optimization techniques. Finally, an example is given to illustrate the proposed results, and comparison with the existing methods is made. 1tab,. 10refs.