Stability Analysis of Switched Systems with 'Mixed'-Negative Imaginary Property

Abstract

This paper discusses the stability of feedback systems in which both plant and controller are switched. Switched systems considered here have all their subsystems satisfying the 'mixed'-negative imaginary property. A definition for dissipativity (for switched systems) is proposed, and dissipative switched systems are shown to be stable (under certain conditions). Switched systems with 'mixed'-negative imaginary property are shown to be dissipative and conditions for stability are derived. As an illustration of the results, a switched controller is designed for a nanopositioning stage, which has a 'mixed'-negative imaginary frequency response function. Simulations show that the closed loop is stable and the designed controller damps the resonances satisfactorily.