一类非线性系统的周期间歇镇定

Stabilization of a class of nonlinear systems by using periodic intermittent control

周期间歇控制是一类特殊形式的切换控制,周期间歇控制下的动态系统可视为由一个受控子系统和一个自由子系统组成的周期切换系统。针对周期间歇控制系统动态特征,提出运用时变切换Lyapunov函数方法研究一类非线性系统的周期间歇镇定问题。在控制器激活区间和控制器关闭区间,分别引入不同的时变Lyapunov函数来分析系统的稳定性。利用凸组合技术,将系统稳定性条件表示为一组线性矩阵不等式,通过求解该组线性矩阵不等式,容易获得使系统稳定的控制窗口宽度上界。在稳定性分析的基础上,基于一组线性矩阵不等式的可行解,给出了控制增益矩阵的参数化表示。与现有的时不变Lyapunov函数方法相比,所提出的时变切换Lyapunov函数方法能有效地利用系统的动态特性,降低结果的保守性。数值例子验证了文中方法的有效性和优越性。

Periodic intermittent control is a special form of switching control.The dynamical system under periodic intermittent control can be viewed as a periodic switched system consisting of a con-trolled subsystem and a free subsystem.In view of the dynamic characteristics of the periodic inter-mittent control systems, a time-varying switching Lyapunov function based method is proposed to solve periodic intermittent stabilization problem for a class of nonlinear systems.In the intervals that the controller is active and in the intervals that the controller is closed, different time-varying Lya-punov functions are introduced to analyze the stability of the system under consideration.By using convex combination technique, the derived stability condition is formulated into linear matrix ine-qualities so that the upper bound of the width of the control window can be easily obtained by solving the set of linear matrix inequalities.Based on the obtained stability results, a parameterized repre-sentation of the intermittent control gain matrix is presented in terms of the feasible solution of a set of linear matrix inequalities.Compared with the existing time-invariant Lyapunov function based methods, the proposed time-varying switched Lyapunov function method can effectively utilize the dynamic characteristics of the considered system, and thus reduce the conservatives of the achieved＆amp;nbsp;results.A numerical example is presented to show the validity and superiority of the proposed method.