LMI approach to H2 reduction model of switched systems

This paper presents the H₂ model reduction problem for discrete-time switched systems using average dwell-time approach. First, by constructing multiple Lyapunov functions, the exponential stability criterion of switched systems under average dwell-time tau_alpha is established. Then, a reduced-order model for the underlying system is constructed, which guarantees these two models are close in H₂ norm sense. Finally, an example is given to illustrate our results. All the results in this paper are expressed in terms of linear matrix inequalities (LMIs), which can be easily tested with efficient LMI algorithms.