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Stochastic dynamic output feedback stabilization of uncertain stochastic state-delayed systems
H R Karimi1, P Jabehdar Maralani, B Moshiri
1Control and Intelligent Processing Center of Excellence, Dept. of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran. hrkarimi@ut.ac.ir
ISA Transactions
|May 3, 2006
Summary
This study presents a new control method for stabilizing complex systems with time delays and uncertainties. The proposed approach ensures system stability regardless of the delay, offering a robust solution for stochastic systems.
Area of Science:
- Control Theory
- Systems Engineering
- Nonlinear Dynamics
Background:
- Stochastic systems with time delays present significant control challenges.
- Norm-bounded nonlinear uncertainties complicate system stabilization.
- Output feedback control is crucial for practical applications where states are not fully measurable.
Purpose of the Study:
- To design a stochastic dynamic output feedback (SDOF) control for continuous-time state-delayed systems.
- To achieve robust stabilization against norm-bounded nonlinear uncertainties.
- To ensure stability independent of the time delay.
Main Methods:
- Development of a linear, delayless SDOF control law.
- Application of Finsler's lemma for stability analysis.
- Formulation of existence conditions using linear matrix inequalities (LMIs).
Main Results:
- The designed SDOF control guarantees stochastically exponential stability in the mean square.
- Stability is achieved irrespective of the deterministic time delay.
- Necessary and sufficient conditions for control existence are derived.
Conclusions:
- The proposed control design is effective for stabilizing stochastic systems with state delays and uncertainties.
- The LMI-based conditions provide a systematic way to design the controller.
- The approach demonstrates practical applicability through a validated example.