H_∞ controller design for a class of switched linear discrete-time system with polytopic uncertainties

In this article, a new parameter-dependent stability criterion for switched linear discrete-time systems with polytopic uncertainties is provided to correct an error occurring in previous work, and the parameter-dependent idea is extended to ℓ₂ gain analysis problem. Particularly, a less conservative result is proposed by introducing additional slack matrices. Furthermore, the H_∞ control problem is investigated. Due to the online calculation characteristic of parameter-dependent controller, a controller structure with less computation cost is of interest. Aside from the controller with the same form as in some existing results involving matrix multiplication and inversion operators, another simple structure of controller formulated by a convex combination of a set of matrices is proposed, which can reduce the online computation cost significantly. A numerical example and results of simulation performed on the model of two-mass-spring mechanical system are provided to illustrate the theoretical findings within this article.