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Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay
Huijun Gao1, Xiuming Liu, James Lam
1Department of Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China. hjgao@hit.edu.cn
Summary
This study presents improved stability analysis for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays. Novel methods reduce conservatism, enabling effective stabilization for feedback control systems.
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Systems
- Nonlinear Systems Analysis
Background:
- Discrete-time Takagi-Sugeno fuzzy systems are widely used for modeling complex nonlinear dynamics.
- Time-varying state delays introduce significant challenges in stability analysis and controller design.
- Existing methods often suffer from conservatism, limiting their practical applicability.
Purpose of the Study:
- To develop a less conservative delay-dependent stability condition for discrete-time Takagi-Sugeno fuzzy systems with time-varying state delays.
- To propose a delay-dependent stabilization approach for both state feedback and observer-based output feedback control.
- To formulate stability and stabilization conditions using efficiently solvable linear matrix inequalities.
Main Methods:
- Construction of a novel fuzzy Lyapunov function.
- Application of new techniques to derive delay-dependent stability conditions based on delay bounds.
- Development of a parallel distributed compensation (PDC) scheme for stabilization.
- Formulation of conditions as linear matrix inequalities (LMIs).
Main Results:
- An improved, less conservative delay-dependent stability condition was derived, considering lower and upper delay bounds.
- The conservatism was reduced by avoiding specific bounding inequalities for cross-product terms.
- Effective delay-dependent stabilization strategies were developed for state and observer-based output feedback.
- The proposed conditions, formulated as LMIs, were validated through illustrative examples.
Conclusions:
- The proposed methods offer a significant improvement in stability analysis and stabilization for fuzzy systems with time-varying delays.
- The reduced conservatism leads to more practical and effective control designs.
- The LMI-based formulation ensures efficient computation and broad applicability.
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