一类参数不确定广义时滞系统的H∞保性能鲁棒控制

针对一类状态时滞的参数不确定性广义系统,讨论了它的保性能控制问题.目的是对状态时滞的参数不确定广义系统,提出它的时滞无关保性能鲁棒控制器的一个设计方法.首先给出了广义时滞系统正则、脉冲自由且稳定的严格线性矩阵不等式表示的时滞无关充分条件;然后采用线性矩阵不等式方法,给出参数不确定性广义时滞系统的时滞无关保性能控制问题可解的一个严格线性矩阵不等式表示的充分条件,在此条件可解时,给出了时滞无关保性能鲁棒控制器表达式,以及相应的可保性能指标.最后给出了所提出方法的应用.

Abstract：

The guaranteed cost control problem is studied for singular systems with time-delay and parameter uncertainty in order to design a delay-independent guaranteed cost controller for singular systems with time-delay and parameter uncertainty. First, a delay-independent sufficient condition is derived, which is expressed by strict linear matrix in-equality (LMI) for singular systems with time-delay to be regular, impulse free and stable. Then, the delay-independent sufficient condition for the existence of guaranteed cost controller is given in terms of strict linear matrix inequalities via LMI approach. When these LMI are feasible, an explicit expression of delay-independent robust guaranteed cost controllers and the corresponding guaranteed cost of the systems are obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.     

一类非线性三阶时滞系统的全局渐近稳定性分析

针对一类非线性三阶时滞系统构造出了一个合理的Lyapunov函数,去除了要求lyapunov函数趋于无穷大这个较强的条件约束,只要求系统正半轨线有界,所得的全局渐近稳定性的充分性结果改进了相关文献的结论.最后给出了例子及仿真说明充分条件的有效性.

Abstract：

In this paper,we construct a better Lyapunov function for the nonlinear third order delay system by onlysupposing that the positive half orbit of the system is bounded.The original strong condition is removed,which demands that the Lyapunov function must trend to infinity.The results have improved the conclusions of relevant literatures.At last,examples are given and simulation is made to show the effectiveness of the sufficient conditions.