Abstract
A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.
Highlights
To simplify stability problems of nonlinear systems, the Takagi-Sugeno (T-S) fuzzy system [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] is generally widely used by merging a group of linear systems and membership functions
Based on the simulation results, this paper provides an effective and useful delay-dependent stability criterion to guarantee the asymptotical stability of T-S fuzzy systems with multiplicative noise in the mean square
A delay-dependent stability criterion for nonlinear stochastic systems described by the T-S fuzzy model with multiplicative noise was investigated in this paper
Summary
To simplify stability problems of nonlinear systems, the Takagi-Sugeno (T-S) fuzzy system [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] is generally widely used by merging a group of linear systems and membership functions. Based on the T-S fuzzy modeling approach, delay-dependent stability criteria [25,26] have been developed for nonlinear systems. The controller design problem of the delayed nonlinear systems was not discussed by [29] due to the conversion of sufficient conditions for satisfying the form of Linear Matrix Inequality (LMI). An extra iterative LMI algorithm [12] was proposed to find a solution to the condition derived by the integral Lyapunov function. An integral Lyapunov-Krasovskii function is proposed to avoid the conservatism caused by the derivative of the membership function. To summarize the contributions of this paper, three points are provided: (1) A novel integral Lyapunov-Krasovskii function is proposed to eliminate the conservatism caused by the derivative of the membership function.
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