Stability of positive switched homogeneous systems based on quasi-time-dependent max-separable Lyapunov function method

Abstract

This article analyzes stability issues of positive switched homogeneous systems (PSHSs) including partial unstable subsystems. The quasi-time-dependent max-separable Lyapunov function is firstly constructed to investigate exponential stability problems for PSHSs with unstable subsystems under mode dependent average dwell time switching rule, which not only covers the previous conclusions but also reduces conservatism in comparison to time-independent results. Besides, stability conditions are accessed conveniently by handling a nonlinear programming. Finally, this paper puts forward a numerical example to illustrate the credibility of findings.