Determining Dissipativity of Switched Nonlinear Systems Using Linearization

Abstract

Local strict QSR‐dissipativity of a switched nonlinear system is studied using the linearization technique in this paper. We obtain local strict QSR‐dissipativity of a switched system even if each subsystem is not locally strictly QSR dissipative by designing a switching law. The derived dissipative sufficient condition is characterized by a modified Lyapunov‐Metzler inequality that can be simplified as an LMI by assuming specific forms. Two special forms of local strict QSR‐dissipativity, local input state strict passivity and local L2‐gain, are considered. When the approximate errors of a switched affine system satisfy certain conditions, local strict passivity can be drawn from its linearization. Finally, a numerical example is given to illustrate how to apply the proposed method to achieve passivity of switched nonlinear systems.

Exponential quasi‐(Q,S,R)‐dissipativity and practical stability for switched nonlinear systems

“…Therefore, the dissipativity of the switched nonlinear system was defined using multiple storage functions and the corresponding stability was obtained in. [37][38][39][40][41] Nevertheless, there have been few results on quasi-dissipativity for switched nonlinear systems. 42,43 The framework of quasi-passivity theory for switched nonlinear systems using multiple storage functions and multiple supply rates was set up in.…”

Stability Analysis and L2‐gain of Switched Neutral Systems with All Unstable Subsystems

“…The switched system is a crucial class of hybrid systems, which comprises a family of subsystems and a switching rule accounting for which subsystems will be activated along the system locus at a time instant . Switched neutral system is a particular class of switched systems, which relies on not only the delays of state but also the delays of the state's derivative .…”