Stability properties of reset systems. (English) Zbl 1283.93213

Nešić, Dragan; Zaccarian, Luca; Teel, Andrew R.

Automatica 44, No. 8, 2019-2026 (2008).

Summary: Stability properties for a class of reset systems, such as systems containing a Clegg integrator, are investigated. We present Lyapunov based results for verifying \(\mathcal L_{2}\) and exponential stability of reset systems. Our results generalize the available results in the literature and can be easily modified to cover \(\mathcal L_p\) stability for arbitrary \(p\in[1,\infty]\). Several examples illustrate that introducing resets in a linear system may reduce the \(\mathcal L_{2}\) gain if the reset controller parameters are carefully tuned.

MSC:

93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D20	Asymptotic stability in control theory
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

hybrid systems; nonlinear systems; \(\mathcal L_2\) stability; disturbances

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