Robust filter design for discrete time switched interconnected systems with time-varying delays.

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Interconnected systems (IS) with discrete-time switching exhibit complex dynamics.
• Challenges include time delays, external disturbances, and inherent uncertainties in subsystems.
• Ensuring stability and performance in such systems is critical for reliable operation.

Purpose of the Study:

• To design an appropriate filter for discrete-time $$-linear interconnected systems with uncertain switching.
• To guarantee Exponentially Mean-Square Stability (EMSS) in the presence of time delays and external disturbances.
• To implement $$ performances (HP) for effective disturbance rejection.

Main Methods:

• Utilizing the Lyapunov-Krasovskii functional (LKF) approach.
• Employing the Linear-Matrix-Inequality (LMI) framework for filter synthesis.
• Developing sufficient criteria to ensure system stability.

Main Results:

• Sufficient criteria for Exponentially Mean-Square Stability (EMSS) were successfully developed.
• Filter parameters were systematically determined using the MATLAB-LMI toolbox.
• The designed filter demonstrated effectiveness in handling uncertainties and disturbances.

Conclusions:

• The proposed filter design effectively addresses the challenges of uncertain discrete-time switching in interconnected systems.
• The LKF and LMI-based approach provides a robust method for achieving guaranteed stability and performance.
• The study validates the filter's efficacy through practical mathematical examples.