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Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 4082–4089 | Cite as

Bounded Real Lemma for 2-D Discrete Systems Using Asymmetric Lyapunov Matrix: What Shall It Be?

  • Neha Agarwal
  • Haranath Kar
Short Paper
  • 76 Downloads

Abstract

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.

Keywords

Bounded real lemma Fornasini–Marchesini second model \(H_\infty \) control Lyapunov stability Two-dimensional (2-D) linear discrete system 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringMotilal Nehru National Institute of Technology AllahabadAllahabadIndia

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