The Controllability And Observability Of Nonlinear Discrete Control Systems

This paper mainly concerns the controllability and observability of nonlinear dis-crete control systems. By introducing Fredholm operator and coincidence degree the-ory, sufficient conditions for nonlinear discrete control systems to be completely con-trollable are presented. Specially, if nonlinear part of systems satisfies some condi-tions, then we can establish sufficient and necessary conditions guaranteeing the null-controllability of nonlinear discrete control systems. At the same time, we study the local observability of nonlinear discrete control systems using Brouwer’s fixed point theorem. In our approach, the linear part of systems under consideration might admit some degeneracy. In addition, applications are given to illustrate the obtained results.