RMS gain with dwell time for discrete-time switched linear systems

This paper deals with discrete-time systems and considers the problem of computing an upper bound to the dwell time of switched systems ensuring a pre-specified root mean square gain (RMS). As a natural consequence of treating general systems of this particular class in terms of the order and the number of subsystems, only sufficient conditions are worked out. However, as positive features, they are expressed through linear matrix inequalities (LMI) being thus numerically solvable in polynomial time and allows the treatment of stable switched linear systems which do not admit a common Lyapunov function. The case of a guaranteed RMS for arbitrary switching signals is also addressed. The conservativeness of the proposed design method is evaluated by comparison with an easy to calculate lower bound on the minimum dwell time that assures the specified R. level. An simple example constituted by two second order subsystems is included for illustration and to evaluate the conservativeness of the proposed design method.