Regular Papers

International Journal of Control, Automation and Systems 2019; 17(2): 405-414

Published online January 18, 2019

https://doi.org/10.1007/s12555-017-0299-4

© The International Journal of Control, Automation, and Systems

Linear Matrix Inequality Approach to Stochastic Stabilization of Networked Control System with Markovian Jumping Parameters

Yanpeng Wu and Ying Wu*

Xi’an Shiyou University

Abstract

This paper is concerned with the stochastic stabilization problem for a class of networked control system (NCS) with destabilizing transmission factors. By introducing the effective sampling instant to model random time delays and successive packet dropouts as two independent Markov chains, NCS is modeled as a discrete-time Markovian jump linear system with mixed integrated Markovian jumping parameters. In this way, a novel framework to analyze the stochastic stabilization problem of NCS is provided. The necessary and sufficient conditions for the stochastic stabilization of the NCS are obtained by the Lyapunov method and the state-feedback controller gain that depends on the delay modes is obtained in terms of the linear matrix inequalities (LMIs) formulation via the Schur complement theory. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method."

Keywords Linear matrix inequality, Markov chain, networked control system, stochastic stability, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2019; 17(2): 405-414

Published online February 1, 2019 https://doi.org/10.1007/s12555-017-0299-4

Copyright © The International Journal of Control, Automation, and Systems.

Linear Matrix Inequality Approach to Stochastic Stabilization of Networked Control System with Markovian Jumping Parameters

Yanpeng Wu and Ying Wu*

Xi’an Shiyou University

Abstract

This paper is concerned with the stochastic stabilization problem for a class of networked control system (NCS) with destabilizing transmission factors. By introducing the effective sampling instant to model random time delays and successive packet dropouts as two independent Markov chains, NCS is modeled as a discrete-time Markovian jump linear system with mixed integrated Markovian jumping parameters. In this way, a novel framework to analyze the stochastic stabilization problem of NCS is provided. The necessary and sufficient conditions for the stochastic stabilization of the NCS are obtained by the Lyapunov method and the state-feedback controller gain that depends on the delay modes is obtained in terms of the linear matrix inequalities (LMIs) formulation via the Schur complement theory. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method."

Keywords: Linear matrix inequality, Markov chain, networked control system, stochastic stability, time delay.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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