参数不确定广义大系统的保性能分散控制

Guaranteed cost decentralized control for singular large-scale systems with parameter uncertainty

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.

The problem of guaranteed cost decentralized control for continuous-time singular large-scale systems with a quadratic cost function is considered. The system under discussions is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The aim is to design a state feedback decentralized controller such that the closed-loop system is not only robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost decentralized controllers is also given in terms of linear matrix inequalities （LMIs） via linear matrix inequality approach. When this condition is feasible, the desired state feedback decentralized controller gain matricces can then be obtained. An illustrative example is also proposed to demonstrate the effectiveness of the proposed approach.