Robust stability of uncertain discrete-time singular fuzzy systems

Authors:
Shengyuan Xu;Bo Song;Junwei Lu;James Lam
Affiliations:
Department of Automation, Nanjing University of Science and Technology, Nanjing 210094, PR China;Department of Automation, Nanjing University of Science and Technology, Nanjing 210094, PR China;School of Electrical and Automation Engineering, Nanjing Normal University, 78 Bancang Street, Nanjing 210042, PR China;Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

This paper considers the problem of robust stability analysis of uncertain discrete-time singular fuzzy systems described by a class of extended Takagi-Sugeno fuzzy dynamic models with time-varying norm-bounded parameter uncertainties. A sufficient condition ensuring a discrete singular fuzzy system to be regular, causal and stable is proposed in terms of a set of linear matrix inequalities. Based on this, a robust stability condition is obtained. Both of these conditions can be checked by using recently developed algorithms in solving LMIs. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.