一类不确定广义时滞系统的保性能控制

The Guaranteed Cost Control for a Class of Uncertain Singular Time-delay Systems

研究同时具有状态时滞和控制输入时滞的一类不确定广义系统的保性能控制问题。对于给定的性能指标及所容许的不确定和时滞,设计一个无记忆状态反馈控制律,使得闭环系统是渐近稳定的,闭环系统的性能函数值不大于给定的一个数。利用Lyapunov稳定性定理和线性矩阵不等式工具,得到广义系统的状态反馈保性能鲁棒控制器存在的充分条件和设计方法,并给出相应性能指标上界。仿真示例表明该方法的有效性。

The guaranteed cost control （GCC） problem for a class of uncertain singular systems with state delay and input delay is discussed. Attention is focused on the design of nonmemory state feed back con trollers such that the closed- loop system is asmptotically stable and the closed- loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay. By means of Lyapunov function and linear matrix inequalities （LMIs） technique, a sufficient condition for the existence of the guaranteed controllers is given, and the GCC state feedback controllers are designed. Finally, an illustrative example demonstrates the effectiveness of proposed method.