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Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays
Huaguang Zhang1, Yingchun Wang, Derong Liu
1Institute of Electric Automation, Northeastern University, Shenyang 110004, China. hgzhang@ieee.org
Summary
This study presents a new method for guaranteed cost control in uncertain stochastic nonlinear systems with time delays. The approach ensures system stability and performance despite uncertainties, offering a robust solution for complex control problems.
Area of Science:
- Control Theory
- Systems Engineering
- Fuzzy Logic
Background:
- Stochastic nonlinear systems with multiple time delays present significant control challenges.
- Uncertainties and time delays can degrade system performance and stability.
- Guaranteed cost control aims to minimize a cost function while ensuring stability.
Purpose of the Study:
- To develop a delay-dependent guaranteed cost control strategy for uncertain stochastic nonlinear systems.
- To address control problems involving Takagi-Sugeno fuzzy models with uncertain parameters.
- To provide conditions for the existence of an optimal guaranteed cost controller.
Main Methods:
- Construction of a novel stochastic Lyapunov-Krasovskii functional.
- Development of sufficient conditions for delay-dependent guaranteed cost control.
- Formulation of controller existence conditions using linear matrix inequalities (LMIs).
Main Results:
- Sufficient conditions for delay-dependent guaranteed cost control were derived without system transformation.
- Conditions for the existence of an optimal guaranteed cost controller were established.
- Simulation examples validated the effectiveness of the proposed control approach.
Conclusions:
- The proposed method offers an effective approach for guaranteed cost control of uncertain stochastic nonlinear systems with time delays.
- The use of a new Lyapunov-Krasovskii functional simplifies the analysis and design.
- The LMI-based conditions facilitate practical controller implementation.
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