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Stability of Interfered Digital Filters Subjected to Markovian Jumping Parameters and Time Delay Employing Quantization/Overflow Nonlinearities

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Abstract

The problem of mixed \(H_{\infty }\) and passivity performance analysis is investigated for interfered digital filters under Markovian jumping parameters, time-varying delays and various combinations of quantization and overflow nonlinearities. By virtue of Lyapunov–Krasovskii stability approach, a novel sufficient condition is derived such that the underlying system is stochastically stable and satisfies a prescribed mixed \(H_{\infty }\) and passivity performance index. In a unified framework, the proposed criterion can be used for the \(H_{\infty }\) performance, the passivity and the mixed \(H_{\infty }\) and passivity performance of digital filters. Moreover, the problem is formulated to obtain optimal performance index (i.e. \(H_{\infty } ,\) passivity and mixed \(H_{\infty }\) and passivity) of interfered digital filters. At last, two numerical examples and an interfered digital filter with tridiagonal state-space model are applied to demonstrate the effectiveness of the proposed approach.

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Acknowledgements

The author is grateful for the constructive comments and suggestions of the editors and reviewers. The author would like to especially thank Professor Haranath Kar for their valuable suggestions.

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  1. Department of Electronics & Communication Engineering, C. V. Raman Global University, Bhubaneswar, 752054, India

    Mani Kant Kumar

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Correspondence to Mani Kant Kumar.

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Kumar, M.K. Stability of Interfered Digital Filters Subjected to Markovian Jumping Parameters and Time Delay Employing Quantization/Overflow Nonlinearities. Circuits Syst Signal Process 41, 892–914 (2022). https://doi.org/10.1007/s00034-021-01808-4

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  • DOI: https://doi.org/10.1007/s00034-021-01808-4

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