Reference
S. Yuan, L. Zhang, B. De Schutter, and S. Baldi, "A novel Lyapunov function for
a non-weighted
L2 gain of asynchronously
switched linear systems,"
Automatica, vol. 87, pp.
310-317, Jan. 2018.
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.
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BibTeX
@article{YuaZha:17-015,
author = {Yuan, Shuai and Zhang, Lixian and De Schutter, Bart and Baldi,
Simone},
title = {A Novel {Lyapunov} Function for a Non-Weighted {$\mathcal{L}_2$}
Gain of Asynchronously Switched Linear Systems},
journal = {Automatica},
volume = {87},
pages = {310--317},
month = jan,
year = {2018}
}