Output-Dependent Switching Control of Linear Systems with Dwell Time

A unified approach to output-dependent switching law synthesis with dwell time is presented. This approach guarantees the asymptotic stability and achieves a prescribed upper-bound on the L₂-gain of switched linear systems. When the dwell time is zero, the approach recovers, as special cases, the results of the known methods of minimizing the Lyapunov function and its derivative. Two switching laws emerge from the developed theory. The first switching law depends directly on the measurements, without applying any filter. At the cost of an added conservatism, this switching law can be designed without applying tuning parameters. The second switching law applies a filter; the switching law depends then on the filter’s states. Two examples are given that demonstrate the application of the proposed design methods.