Reduction model of a class of discrete switched linear systems: An LMI approach

This paper investigates the H₂ model reduction problem for a class of linear discrete-time switched systems. By applying the piecewise Lyapunov functional approach and linear matrix inequality (LMI) technique, the exponential stability criterion of switched systems under average dwell-time is established. For particular original discrete-time switched systems, the corresponding reduction-order models are constructed so as to ensure the exponential stability of the error systems and to achieve prescribed H₂ performance. A numerical example illustrates the effectiveness of the proposed methods.