Viability Analysis for Nonlinear System Based on Stability and Passivity

The viability problem for general nonlinear systems is investigated. First,the necessary and sufficient conditions for determining the viability of the nonlinear system on a region expressed by an inequality are developed using the viability theory based on differential inclusions. Next,it is proved that the Lyapunov stability for the nonlinear system on the equilibrium is equivalent to the viability of the system on arbitrary Lyapunov function level sets,and it is determined that the Lyapunov function level set is the viable domain. In addition,on the basis of passivity,it is also proved that through the appropriate output feedback,the system can be made viable on the region determined by the storage function,and at the same time,the viable domain is acquired. Finally,the simulation results show the correctness of the conclusions.