Stability Analysis for a Type of Multiswitching System with Parallel Structure

Zhang Yan, Liu Yongqiang and Liu Yang

Mathematical Problems in Engineering, 2018, vol. 2018, 1-16

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:3834601

DOI: 10.1155/2018/3834601

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