A novel Lyapunov function for a non-weighted L2 gain of asynchronously switched linear systems
Shuai Yuan (TU Delft - Mechanical Engineering)
Lixian Zhang (Harbin Institute of Technology)
Bart De Schutter (TU Delft - Mechanical Engineering)
Simone Baldi (TU Delft - Mechanical Engineering)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
In this paper, a novel Lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes. The novelty consists in continuity of the Lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched. This structure is exploited to construct a time-varying Lyapunov function that is non-increasing at time instants of discontinuity. Stability criteria based on the novel Lyapunov function are developed to guarantee global asymptotic stability in the noiseless case. Most importantly, when exogenous disturbances are considered, the proposed Lyapunov function can be used to guarantee a finite non-weighted L2 gain for asynchronously switched systems, for which Lyapunov functions proposed in literature are inconclusive. A numerical example illustrates the effectiveness of the proposed method.
help_outline