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An LMI Based Criterion for Global Asymptotic Stability of Discrete-Time State-Delayed Systems with Saturation
1Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Chennai 600 127, India.
International Scholarly Research Notices
|July 20, 2016
Summary
This study introduces a new criterion using linear matrix inequalities (LMIs) to ensure the stability of discrete-time systems with delays and saturation. Numerical examples demonstrate the method's effectiveness.
Area of Science:
- Control theory
- Systems engineering
- Nonlinear systems analysis
Background:
- Discrete-time systems are fundamental in modern control applications.
- State-delays and saturation nonlinearities introduce significant challenges in stability analysis.
- Existing methods may not effectively handle systems with both multiple delays and saturation.
Purpose of the Study:
- To develop a novel criterion for guaranteeing global asymptotic stability.
- To address discrete-time systems incorporating multiple state-delays and saturation nonlinearities.
- To provide a computationally tractable method for stability assessment.
Main Methods:
- Formulation of a stability criterion based on linear matrix inequalities (LMIs).
- Analysis of systems with multiple time-varying state-delays.
- Inclusion of input or state saturation nonlinearities within the stability framework.
Main Results:
- A new LMI-based criterion for global asymptotic stability is successfully derived.
- The criterion is applicable to discrete-time systems with multiple state-delays and saturation.
- Numerical examples validate the effectiveness and applicability of the proposed criterion.
Conclusions:
- The proposed LMI-based criterion offers a robust approach for analyzing the stability of complex discrete-time systems.
- This work contributes to the advancement of control theory for systems with delays and nonlinearities.
- The presented method provides a practical tool for engineers designing and analyzing such systems.
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