一类不满足匹配条件的不确定广义系统的最优保性能控制

Optimal Guaranteed Cost Control for a Class of Singular Systems with Mismatched Uncertainties

针对一类不确定性是范数有界时不变的可不满足匹配条件的参数不确定广义线性系统和一个二次型性能指标,研究了其状态反馈最优保性能控制器的设计问题.采用线性矩阵不等式方法,导出了一个用线性矩阵不等式表达的保性能控制律存在的充分条件;在此基础上,建立并求解一个凸优化问题,给出了最优保性能控制律的设计方法.通过实例说明了该方法的应用.

For a class of continuous-time singular linear systems with normal bounded timeunvarying and mismatched parameter uncertainties and a quadratic cost index, the problem of designing an optimal guaranteed cost state feedback controller is discussed in this paper. A sufficient condition for the existence of guaranteed cost controller is derived in terms of linear matrix inequalities （LMIs）. Besides, the design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques. Finally, an example is given to illustrate the results.