Fuzzy modal time-scheduled control and L₂-gain analysis for switched nonlinear systems

Area of Science:

• Control Theory
• Nonlinear Systems
• Fuzzy Logic

Background:

• Switched nonlinear systems present challenges in stability and control due to their hybrid nature.
• Achieving guaranteed performance, such as L2-gain, is crucial for practical applications.

Purpose of the Study:

• To develop a fuzzy modal time-scheduled control (FMTSC) strategy for switched nonlinear systems.
• To establish criteria for H-infinity performance in systems with both stable and unstable subsystems.
• To introduce time-scheduled multiple discontinuous Lyapunov functions (TMDLFs) for switched Takagi-Sugeno (T-S) fuzzy systems.

Main Methods:

• Hybrid dwell time method combined with fuzzy modal control.
• Development of time-scheduled multiple discontinuous Lyapunov functions (TMDLFs).
• Analysis of H-infinity performance for switched systems.

Main Results:

• A novel switched fuzzy modal time-scheduled control (FMTSC) strategy is proposed.
• A criterion for H-infinity performance is established for systems with mixed stability properties.
• The effectiveness of TMDLFs is demonstrated for switched T-S fuzzy systems with L2-gain properties.

Conclusions:

• The proposed FMTSC strategy effectively addresses the control problem for switched nonlinear systems.
• The developed theoretical results are validated through comparative and practical examples.
• The study contributes to the advancement of robust control techniques for complex hybrid systems.