Event-triggered observer-based H_∞ sliding mode control of nonlinear systems

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear System Analysis

Background:

• Takagi-Sugeno fuzzy models are widely used for nonlinear systems.
• State observers are crucial for systems with unmeasured states.
• Event-triggering mechanisms and signal delays pose significant control challenges.

Purpose of the Study:

• To develop a sliding mode control (SMC) strategy for nonlinear one-sided Lipschitz systems based on Takagi-Sugeno fuzzy models.
• To address challenges of unavailable states and signal delays in control design.
• To guarantee finite-time reachability and stability with H-infinity performance.

Main Methods:

• Design of a state observer utilizing an event-triggering mechanism.
• Proposal of an integral sliding surface based on estimated states.
• Application of the equivalent control principle to derive sliding mode dynamics.
• Construction of a sliding mode controller ensuring finite-time convergence.
• Stability analysis using Lyapunov functions and H-infinity performance criteria, formulated via Linear Matrix Inequalities (LMIs).

Main Results:

• Finite-time reachability of the predefined sliding surface is guaranteed.
• The stability of the sliding mode dynamics is confirmed with H-infinity performance.
• LMIs are established for controller synthesis and performance verification.
• Numerical examples demonstrate the efficacy of the proposed control method.

Conclusions:

• The proposed event-triggered sliding mode control strategy effectively handles nonlinear Takagi-Sugeno fuzzy systems with state estimation and communication delays.
• The method ensures finite-time stability and H-infinity performance, validated through theoretical analysis and simulations.