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Guaranteed performance control of switched linear systems: A differential-Riccati-equation-based approach

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Abstract

This paper studies a quadratic performance certificate in terms of an upper bound and a lower bound for switched linear systems over all admissible dwell-time switching signals. The infinite-horizon performance is reformulated into the summation of the finite-horizon performance for each subsystem over switching intervals that can be calculated by solving a family of differential Riccati equations. The time-varying positive definite solutions are exploited to construct a novel piecewise quadratic Lyapunov function for the closed-loop system, which guarantees that the Lyapunov function is decreasing at and between the switching instants. This decreasing property results in consistency between the piecewise quadratic Lyapunov function for switched systems and standard quadratic Lyapunov function for non-switched systems, based on which an upper bound of the quadratic performance is obtained by referring to the techniques for non-switched systems. In addition, a lower bound is established by solving a family of algebraic Riccati equations. The effectiveness of the guaranteed performance control method is illustrated by making use of a numerical example.

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, China

    Dongzhe Wang, Shuyuan Wang, Shuai Yuan, Bo Cai & Lixian Zhang

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  1. Dongzhe Wang
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  2. Shuyuan Wang
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  3. Shuai Yuan
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  4. Bo Cai
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  5. Lixian Zhang
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Correspondence to Shuai Yuan.

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This work was funded in part by National Natural Science Foundation of China 61322301.

This article is part of the Topical Collection: Special Issue on Networked Cyber-Physical Systems

Guest Editors: Heng Zhang, Mohammed Chadli, Zhiguo Shi, Yanzheng Zhu, and Zhaojian Li

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Wang, D., Wang, S., Yuan, S. et al. Guaranteed performance control of switched linear systems: A differential-Riccati-equation-based approach. Peer-to-Peer Netw. Appl. 12, 1810–1819 (2019). https://doi.org/10.1007/s12083-019-00748-w

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  • DOI: https://doi.org/10.1007/s12083-019-00748-w

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