Stability Analysis for a Type of Multiswitching System with Parallel Structure

Abstract

This paper proposes a new type of multiswitching system and a subsystems-group as a basic switching unit that obeys the law. Unlike traditional switching systems, the system selects multiple subsystems instead of one on each time interval. Thus, a framework of parallel structure organizes the subsystems as a group. A multiswitched system is widely used in engineering for modelling and control; this system reflects the actual industrial dynamical process. Thus, the stability of the system is studied. Assuming that these continuous and discrete-time subsystems are Hurwitz and Schur stable, the subsystems-groups matrices commute each other based on the subsystems matrices pairwise commutative. Then, the multiswitched system is exponentially stable under arbitrary switching, and there exists a common Lyapunov function for these subsystems. The main result is extended to a parallel-like structure; therefore, some stability results are gained under some reasonable assumption. At last, a numeral example is given to illustrate the structure and the stability of this system.