一类非线性多时滞系统的鲁棒镇定

研究在状态及控制变量中均含时滞的一类Ｌｕｒｅ型非线性不确定系统的鲁棒镇定问题，即设计线性控制律，以抑制系统的不确定性、时滞性和Ｌｕｒｅ非线性等因素的影响，从而保证原系统鲁棒稳定。基于Ｌｙａｐｕｎｏｖ稳定性理论，利用奇异值分解的方法，通过求解最优调节器的代数Ｒｉｃｃａｔｉ方程，给出了期望控制律的存在条件和解析表达式，使不确定系统在不同时滞作用下及Ｌｕｒｅ非线性因素影响下仍能达到渐近稳定，为这类问题的解决提供一种途径。

Robust Stabilization of a Class of Nonlinear Multi-time-delay Systems

he problem of robust control for a class of Lure-type nonlinear uncertain systems with time-delay in both state and control variables is studied in this paper. The problem is simply the design of linear control laws which restrict the influence of the uncertainties,time-delay and Lure-type nonlinearities to the designed systems,so that the original systems might be robustly stable. Based on Lyapunov theory, by adopting singular decomposition and resolving the algebraical Riccati equation,the exist condition and explicit expression of desired controll law are given. So the uncertainty system under different time-delay and Lure nonlinear can be still stable asymptotically. From above analysis, a procedure is proposed for solving this type of problems.