Determining the Approximate Viability for Nonlinear Switched Systems

The approximate viability for nonlinear switched systems composed of a finite number of dynamic subsystems is studied.Firstly,a piecewise constant feedback controller is constructed to prove that the system can achieve the approximate viability property under arbitrary switching criterion,and a sufficient condition determining the viability of the systems on an arbitrary set is given.At last,based on the nonsmooth analysis theory,a sufficient viability condition for the systems on a region expressed by inequalities is also provided.