Synthesis of Hybrid Systems with Limit Cycles Satisfying Piecewise Smooth Constraint Equations

摘要

In this paper, we propose a synthesis method of hybrid systems with specified limit cycles. Several methods which sysnthesize a nonlinear system with prescribed limit cycles have been proposed. In these methods, the limit cycle is given by an algebraic equation, which will be called constraint equations, and its stability is guaranteed by a Lyapunov function derived from the constraint equation. In general, limit cycles of hybrid systems are nonsmooth due to the discontinuous vector fields. So the limit cycles are given by piecewise smooth constraint equations, we employ the piecewise smooth Lyapunov functions to construct desired nonsmooth limit cycles and guarantee their stability.