Abstract
The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.
Highlights
The T-S fuzzy modeling approach, as a simple and effective tool for nonlinear control systems, has been widely accepted and extensive studied for a few decades [1,2,3,4,5,6,7,8]
An indirect approach, namely, the inputoutput (IO) approach is introduced to deal with the stability analysis and control design of T-S fuzzy delta operator systems with time-varying delay
The main contribution of paper is that the stability analysis and stabilization problems for fuzzy delta operator systems with time-varying delay are investigated by the IO approach
Summary
The T-S fuzzy modeling approach, as a simple and effective tool for nonlinear control systems, has been widely accepted and extensive studied for a few decades [1,2,3,4,5,6,7,8]. The delta operator model can be applied as a useful approach to deal with discrete-time systems under high sampling rates through the analysis methods of continuous-time systems [19,20,21,22]. To the authors’ best knowledge, few results on the stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are proposed. An indirect approach, namely, the inputoutput (IO) approach is introduced to deal with the stability analysis and control design of T-S fuzzy delta operator systems with time-varying delay. The main contribution of paper is that the stability analysis and stabilization problems for fuzzy delta operator systems with time-varying delay are investigated by the IO approach. The symbol “∗” in a matrix stands for the transposed elements in the symmetric positions
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