Robust observer-based H_∞ control for uncertain discrete singular systems with time-varying delays via sliding mode...

Area of Science:

• Control Systems Engineering
• Systems Theory
• Robust Control

Background:

• Discrete singular systems with time-varying delays present significant control challenges.
• Observer-based control is necessary when system states are unmeasured.
• Sliding Mode Control (SMC) is a robust control technique effective for uncertain systems.

Purpose of the Study:

• To develop a robust observer-based H∞ control strategy for uncertain discrete singular systems with time-varying delays.
• To design a sliding mode controller that ensures system admissibility and an H∞-norm bound.
• To address the issue of chattering in sliding mode control.

Main Methods:

• Sliding Mode Control (SMC) combined with an observer technique.
• Construction of a novel sliding surface based on estimated states.
• Utilization of Lyapunov-Krasovskii functional to derive conditions for stability.
• Formulation of sufficient criteria using solvable Linear Matrix Inequalities (LMIs).

Main Results:

• A full-order closed-loop system is generated using estimated states.
• New sufficient criteria for system admissibility and H∞-norm bound are derived.
• A sliding mode controller is obtained by solving the LMI, ensuring reaching motion and reduced chattering.
• Theoretical results are validated through numerical simulations.

Conclusions:

• The proposed observer-based H∞ control strategy effectively handles uncertain discrete singular systems with time-varying delays.
• The developed method ensures system admissibility and achieves a guaranteed H∞-norm bound.
• The approach successfully reduces chattering while maintaining robust performance.