一类不确定非线性时滞系统的可靠保成本控制

摘要

The problem of reliable guaranteed cost control is investigated for nonlinear uncertain time-delay systems against actuator failure.Based on Lyapunov stability theory,a sufficient condition for the existence of reliable guaranteed cost control is derived and transformed to a Linear Matrix Inequality.At the same time,the associated designing approach of the state-feedback controller id offered.The cost is relevant to time delay.The resultant reliable guaranteed cost control systems not only retain asymptotic stability but also possess the performance index of guaranteed cost despite any outages within a prespecified subset of actuators.Finally,a numerical example was presented to illustrate the validity and feasibility of this approach.%针对包含时滞的一类非线性不确定系统,在执行器可能发生故障的情况下,研究了此类系统可靠控制器的设计和成本上界的确定问题.从Lyapunov定理出发,经演绎后得到可靠控制器和成本有界需要满足的矩阵不等式,通过利用Schur补定理,将矩阵不等式化为标准的LMI,同时给出了系统控制器和成本上界.闭环控制器能够使得系统在执行器失效时系统对允许的不确定性具有容错能力,且保成本上界的存在.最后通过给出一个系统实例,检验了所提出方法的可应用性.