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New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning
Pavin Mahmoudabadi1, Mokhtar Shasadeghi1, Jafar Zarei1
1Faculty of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran.
ISA Transactions
|July 16, 2017
Summary
This study enhances nonlinear system stability analysis using Takagi-Sugeno fuzzy models and interval time-varying delays. New methods reduce conservatism for improved stability criteria and controller design.
Area of Science:
- Control Systems Engineering
- Nonlinear Dynamics
- Fuzzy Logic Systems
Background:
- Nonlinear systems with time-varying delays present significant control challenges.
- Takagi-Sugeno (T-S) fuzzy models offer a framework for analyzing such systems.
- Interval time-varying delays introduce complexities in stability analysis.
Purpose of the Study:
- To develop less conservative stability criteria for nonlinear systems with interval time-varying delays.
- To design controllers for stabilizing these systems using a parallel distributed compensation (PDC) scheme.
- To improve the feasibility region for stability analysis.
Main Methods:
- Utilizing a delay-partitioning approach for integral terms within the Lyapunov-Krasovskii functional (LKF).
- Employing a fuzzy Lyapunov function and introducing slack matrix variables.
- Applying Jensen's integral inequality for handling integral terms.
- Formulating stability and stabilization conditions in terms of linear matrix inequality (LMI).
Main Results:
- New, less conservative delay-dependent stability criteria are derived.
- The proposed methods expand the design space for controller synthesis.
- Stability and stabilization conditions are achieved with reduced conservatism.
- Effectiveness demonstrated through two numerical examples.
Conclusions:
- The proposed approach provides a more effective method for stability analysis and controller design of nonlinear systems with interval time-varying delays.
- The use of LMI formulation ensures computational tractability.
- The results offer significant improvements over existing methods in terms of conservatism reduction.
Keywords:
Delay-partitioning approachFuzzy Lyapunov functionLinear matrix inequality (LMI)T-S fuzzy systemTime-varying delayMore Related Videos
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