Robust guaranteed cost control for singular Markovian jump systems with time-varying delay

Area of Science:

• Control Systems Engineering
• Stochastic Systems Analysis
• Nonlinear Dynamics

Background:

• Singular Markovian jump systems are complex dynamical systems with applications in various fields.
• Time-varying delays introduce significant challenges in stability analysis and controller design.
• Guaranteed cost control aims to minimize a cost function while ensuring stability.

Purpose of the Study:

• To develop a novel guaranteed cost control strategy for continuous-time singular Markovian jump systems with time-varying delays.
• To derive delay-range-dependent conditions for regularity, absence of impulses, and mean-square exponential stability.
• To propose an effective state feedback controller design method with reduced conservatism.

Main Methods:

• Utilizing strict linear matrix inequality (LMI) formulations.
• Developing delay-range-dependent stability criteria.
• Avoiding the use of free-weighting matrices for improved efficiency.
• Designing a guaranteed cost state feedback controller.

Main Results:

• A delay-range-dependent LMI condition is established to guarantee system regularity, absence of impulses, and mean-square exponential stability.
• The proposed method achieves an H(∞) performance level.
• The existence condition for the guaranteed cost state feedback controller is successfully derived.
• A numerical example demonstrates the effectiveness and reduced conservatism of the controller design.

Conclusions:

• The developed LMI-based approach provides a less conservative and effective method for guaranteed cost control of singular Markovian jump systems with time-varying delays.
• The controller design ensures desirable system properties including regularity, absence of impulses, and stability.
• The findings contribute to the advancement of robust control theory for complex dynamical systems.