Optimized state-dependent switching law design for a class of switched nonlinear systems with two unstable subsystems

Yusheng Zhou and Danhong Chen

Applied Mathematics and Computation, 2021, vol. 397, issue C

Abstract: This paper proposes a new method for designing a state-dependent switching law to stabilize a class of switched nonlinear system with two unstable subsystems. The main idea is to convert each subsystem to a second-order mechanical system by introducing a reversible transformation, thus the summation of its kinetic and potential energies is calculated as an energy function. Then, by defining a performance index with energy function and using the variational principle, two optimal switching curves are derived from the Euler equation. By adopting a switching law designed by such switching curves, the state of the switched system can approach to the origin at the fastest speed in a sense. In addition, for the case of switched systems with linear vibration subsystems, a critical stability condition related to the stiffness and negative damping coefficients of the subsystems is obtained to make the switched system periodic. Finally, simulation results show that the proposed method can effectively solve the stability problem of switched systems, in which each subsystem does not have any stability factors.

Keywords: Switched nonlinear system; Unstable subsystem; State-dependent switching law; Optimal switching curve; Variational principle; Periodic solution (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308250

DOI: 10.1016/j.amc.2020.125872

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