一类双线性不确定时滞系统的鲁棒控制

Robust Control for Uncertain Bilinear Systems with Time Delays

双线性系统是最接近线性系统的一类非线性系统,时滞现象和不确定性是实际系统中最常见的现象.而对时滞系统和对不确定系统的研究一直是控制界研究的热点问题.研究了一类既有状态时滞,又有控制时滞的多时滞不确定双线性系统,通过构造Lyapunov泛函,讨论该Lyapunov泛函沿着该双线性系统的导数,给出了这类系统时滞无关鲁棒镇定的条件.利用Lyapunov和Riccati方程的解,构造了线性鲁棒状态反馈控制器.

Bilinear system is a class of nonlinear systems,which is closest to the linear system.Time delay and uncertainty are the most common phenomena in the actual system.It has been a hot research topic in control community to study time delay systems and uncertain systems.The uncertain bilinear systems with multiple time delays in both system state and control are studied.The derivate of Lyapunov function along the bilinear systems is researched.The condition for robust stabilizable independent of delay of the systems is given.Using solutions of Lyapunov and Riccati equations,a linear state feedback control law is proposed.