Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

Abstract

This paper concerns managing the robust exponential stability problem of uncertain Takagi–Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov–Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.

Keywords:

• T–S fuzzy systems
• Lyapunov–Krasovskii functional
• linear matrix inequalities (LMIs)
• maximum allowable upper bound (MAUB)

Acknowledgments

The authors would like to thank the editors and the reviewers for their valuable suggestions and comments which have led to a much improved paper.

Disclosure statement

No potential conflict of interest was reported by the author.