Positive \(L_{1}\) Controller Design for Positive Piecewise Homogeneous Markovian Jump Systems

  • Di Zhang
  • Qingling Zhang
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)


This paper introduces a problem of positive \(L_{1}\) controller design for positive piecewise homogeneous Markovian jump system. The difference with the existing achievements is that the considered transition rates of positive Markovian jump system is time-varying. This time-varying nature is finite piecewise homogeneous. The controller is designed by intentionally introducing a proper delay, this method considers the information about the current and delayed state. The obtained closed-loop system is positive piecewise homogeneous Markovian jump system with time-delay. Firstly, by means of choosing a linear co-positive Lyapunov function, stochastic stability and \(L_{1}\) performance are analyzed for positive piecewise homogeneous Markovian jump system with time-delay. Then, based on the obtained achievements, positive \(L_{1}\) controller is designed for positive piecewise homogeneouss Markovian jump system. Finally, a numerical example is considered to illustrate the effectiveness of theoretical results.


Piecewise homogeneous Markov process Positive Markovian jump systems Controller design 


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Authors and Affiliations

  1. 1.Institute of Systems ScienceState Key Laboratory of Synthetical Automation for Process Industries, Northeastern UniversityShenyangChina

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