Mixed H and passivity-based resilient controller for nonhomogeneous Markov jump systems

M Sathishkumar., R. Sakthivel, Faris Alzahrani, B. Kaviarasan, Yong Ren

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, the robust mixed H and passivity-based control problem is investigated for a class of discrete-time Markov jump nonlinear systems with uncertainties, quantization and time-varying transition probabilities. In addition, the time-varying transition probability matrices in the considered system are described by a polytope set. Further, the measurement size reduction technique is implemented which consists of two factors, namely, the logarithmic quantization and the measurement element selection scheme. In order to reflect the imprecision in controller implementation, the additive controller gain problem is considered. Based on the Lyapunov stability theory, a new set of conditions is derived such that the resulting closed-loop Markov jump system is stochastically stable with a prescribed mixed H and passivity performance index. Finally, the effectiveness of the proposed control scheme is illustrated by two numerical examples including an application example based on a DC motor device.

Original languageEnglish
Pages (from-to)86-99
Number of pages14
JournalNonlinear Analysis: Hybrid Systems
Volume31
DOIs
Publication statusPublished - 2019 Feb 1

Fingerprint

Markov Jump Systems
Passivity
Quantization
Time-varying
Passivity-based Control
Jump System
Controller
Transition Probability Matrix
Controllers
DC Motor
DC motors
Imprecision
Lyapunov Stability Theory
Performance Index
Transition Probability
Polytope
Closed-loop
Nonlinear systems
Control Problem
Logarithmic

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Analysis
  • Computer Science Applications

Cite this

Sathishkumar., M ; Sakthivel, R. ; Alzahrani, Faris ; Kaviarasan, B. ; Ren, Yong. / Mixed H and passivity-based resilient controller for nonhomogeneous Markov jump systems In: Nonlinear Analysis: Hybrid Systems. 2019 ; Vol. 31. pp. 86-99.
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Mixed H and passivity-based resilient controller for nonhomogeneous Markov jump systems . / Sathishkumar., M; Sakthivel, R.; Alzahrani, Faris; Kaviarasan, B.; Ren, Yong.

In: Nonlinear Analysis: Hybrid Systems, Vol. 31, 01.02.2019, p. 86-99.

Research output: Contribution to journalArticle

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AB - In this paper, the robust mixed H ∞ and passivity-based control problem is investigated for a class of discrete-time Markov jump nonlinear systems with uncertainties, quantization and time-varying transition probabilities. In addition, the time-varying transition probability matrices in the considered system are described by a polytope set. Further, the measurement size reduction technique is implemented which consists of two factors, namely, the logarithmic quantization and the measurement element selection scheme. In order to reflect the imprecision in controller implementation, the additive controller gain problem is considered. Based on the Lyapunov stability theory, a new set of conditions is derived such that the resulting closed-loop Markov jump system is stochastically stable with a prescribed mixed H ∞ and passivity performance index. Finally, the effectiveness of the proposed control scheme is illustrated by two numerical examples including an application example based on a DC motor device.

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