Worst case control of uncertain jumping systems with multi-state and input delay information

Authors:
Peng Shi;Magdi S. Mahmoud;Jianqiang Yi;Abdulla Ismail
Affiliations:
Division of Mathematics and Statistics, School of Technology, University of Glamorgan, Pontypridd, Wales CF37 1DL, United Kingdom;College of Engineering, UAE University, P.O. Box 17555, Al-Ain, United Arab Emirates;Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, China;College of Engineering, UAE University, P.O. Box 17555, Al-Ain, United Arab Emirates
Venue:
Information Sciences: an International Journal
Year:
2006

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Abstract

In this paper, the problem of worst case (also called H"~) Control for a class of uncertain systems with Markovian jump parameters and multiple delays in the state and input is investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factors are unknowns and time-varying with known bounds. Complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak-delay dependent stochastic stability with a prescribed H"~-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities (LMIs). Application of the developed theory to a typical example has been presented.