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Robust H ∞ control of uncertain linear impulsive stochastic systems
Author(s) -
Chen WuHua,
Wang JunGe,
Tang YouJian,
Lu Xiaomei
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1286
Subject(s) - control theory (sociology) , robust control , mathematics , parametric statistics , discrete time and continuous time , linear matrix inequality , dwell time , exponential stability , mathematical optimization , computer science , control system , control (management) , nonlinear system , engineering , medicine , clinical psychology , statistics , physics , quantum mechanics , artificial intelligence , electrical engineering
This paper develops robust stability theorems and robust H ∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H ∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

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