Stability analysis and controller design for discrete-time periodic nonlinear quadratic systems

The problems of stability analysis and controller design for discrete-time periodic nonlinear quadratic systems are investigated. Firstly, by using Lyapunov function and the concept of periodic invariant set, a sufficient condition for guaranteeing that the assigned polytope belongs to the domain of attraction of the zero equilibrium point. Secondly, it is also show that this problem is related to the problem of finding a state feedback law and an admissible initial condition domain such that the resulting closed-loop system is asymptotic stability for every initial condition from the admissible domain. The proposed algorithm requires the solution of a suitable feasibility problem involving linear matrix inequalities constraints. Finally, two simulation examples are presented to show the effectiveness of the proposed approach.