Stability analysis and controller design for quadratic discrete-time systems with time delay

摘要

This study aims at investigating the issues of stability and stabilization for time delay quadratic discrete-time systems. First of all, provided a locally asymptotically stable zero equilibrium point of the quadratic system and some other polytope in the state space containing the origin, a delay-independent sufficient condition judging whether this polytope belongs to the domain of attraction (DA) of the equilibrium is obtained. In the second place, it is also show that this issue is related to the problem of devoting to finding a state feedback law and an admissible initial condition domain so that the resulting closed-loop system is asymptotic stability for every initial condition from the admissible domain. Both the issues referred to above can be solved by a set of linear matrix inequalities. In the end, two numerical examples are provided to show the effectiveness of the proposed methodology in this paper.