Computation of H∞ norm for discrete-time symmetric descriptor systems

This paper is devoted to the problem of H_∞ norm computation for discrete-time symmetric descriptor systems. Firstly, we present new versions of the bounded real lemma for the discrete-time systems and generalized bounded real lemma for the discrete-time descriptor systems. Then, we give the explicit expression to H_∞ norm for discrete-time symmetric more general systems and discrete-time symmetric descriptor systems. The results have obvious computational advantages, especially for large scale symmetric systems. Finally, two numerical examples are given to illustrate the results.