基于类Lyapunov函数的非线性切换系统的Reach-While-Stay性质验证

Verifying Reach-While-Stay Property of Nonlinear Switched System Based on Lyapunov-Like Function

考虑了一类连续时间切换系统在任意切换信号下的Reach-While-Stay性质验证问题,提出了基于类Lyapunov函数的验证方法.首先,利用不变集构建了新的RWS性质判定准则,将RWS性质验证问题转化为关于类Lyapunov函数的非线性约束求解问题,然后运用平方和松弛进行编码,进而将其转化为双线性矩阵不等式问题并应用迭代的半定规划进行求解.最后,通过实例表明了该方法的可行性和有效性.

This paper presents a Lyapunov-like function based method for verifying the reach-while-stay property of continuous-time switched systems with arbitrary switching.It first utilizes invariant sets to construct a new type of Lyapunovlike functions,whose existence guarantees the reach-while-stay specification.It then gives a computational approach,combining sum of squares relaxation with sequential semidefinite programming,to solve the constrained optimization problem coming from verification conditions of Lyapunov-like functions.An illustrative example is presented to demonstrate the effectiveness of the proposed method.