Stability analysis of switched systems with 'mixed'-negative imaginary property

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.