Quasi-time-Dependent $$l_2-l_\infty $$ Filtering of Discrete-Time Switched Systems with Admissible Edge-Dependent Average Dwell Time

Abstract

The $$l_2-l_{\infty }$$ filtering problem is studied for a class of discrete-time switched systems under the admissible edge-dependent average dwell time (AED-ADT) switching. Firstly, a new multiple convex Lyapunov function (MCLF) is established as a convex combination form in the context of the $$l_2-l_{\infty }$$ filtering problem. Then, corresponding to the MCLF, the quasi-time-dependent switched filter is proposed for the considered switched system, and the sufficient conditions are derived to ensure that the filtering error system is globally uniformly exponentially stable with a prescribed $$l_2-l_{\infty }$$ performance index. Owing to the quasi-time-dependent and multi-degree-of-freedom properties of the designed switched filter, the wider feasibility regions of system parameters, more desirable $$l_2-l_{\infty }$$ disturbance attenuation levels and tighter bounds on the AED-ADT can be acquired. Finally, a numerical example is given to expound that our approach outperforms the extant results.