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H∞ and dwell time specifications of switched linear systems

This paper deals with continuous-time systems and addresses the problem of characterizing open-loop switching strategies, based on dwell time specification, assuring 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 allow the treatment of stable switched linear systems which do not admit a common Lyapunov function. 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 H∞ level. An example is included for illustration.