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Robust Optimal \(H_\infty \) Control for 2-D Discrete Systems Using Asymmetric Lyapunov Matrix

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Abstract

This paper is concerned with the design of optimal \(H_\infty \) static-state feedback controller for an uncertain 2-D discrete system described by the Fornasini–Marchesini second model. The parametric uncertainties are assumed to be norm bounded. The main contribution of the paper lies in the application of the bounded real lemma derived using a more generalized asymmetric Lyapunov matrix. Based on the derived bounded real lemma, a linear matrix inequality (LMI)-based sufficient condition for the existence of \(H_\infty \) static-state feedback controller is established. Furthermore, convex optimization problem with LMI constraints is formulated to design the optimal \(H_\infty \) static-state feedback controller which not only guarantees the asymptotic stability of the closed-loop system but also achieves optimized noise attenuation level \(\gamma \) for all admissible parametric uncertainties. Finally, with the help of various examples, it is demonstrated that the optimized noise attenuation level \(\gamma \) is better achievable by using asymmetric Lyapunov matrix than using symmetric Lyapunov Matrix.

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Acknowledgements

The authors would like to give sincere thanks to the Editor-in-Chief, associate editor and to the anonymous reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology, Allahabad, 211004, India

    Abhay Vidyarthi, Manish Tiwari & Amit Dhawan

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  1. Abhay Vidyarthi
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  2. Manish Tiwari
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  3. Amit Dhawan
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Correspondence to Abhay Vidyarthi.

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Vidyarthi, A., Tiwari, M. & Dhawan, A. Robust Optimal \(H_\infty \) Control for 2-D Discrete Systems Using Asymmetric Lyapunov Matrix. Circuits Syst Signal Process 36, 3901–3918 (2017). https://doi.org/10.1007/s00034-017-0495-8

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