Bounded Real Lemma for 2-D Discrete Systems Using Asymmetric Lyapunov Matrix: What Shall It Be?
In this paper, we examine a recently reported bounded real lemma for two-dimensional (2-D) discrete systems using asymmetric Lyapunov matrix (Vidyarthi et al. in Circuits Syst Signal Process 36(10):3901–3918, 2017). It is shown that the bounded real lemma, as it is, is incorrect and may lead to erroneous conclusion. Moreover, various corrected and equivalent forms of their bounded real lemma are discussed.
KeywordsBounded real lemma Fornasini–Marchesini second model \(H_\infty \) control Lyapunov stability Two-dimensional (2-D) linear discrete system