Pole assignment stabilization for a class of switched nonlinear time-varying delay systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Systems Theory

Background:

• Switched nonlinear systems with time-varying delays present significant control challenges.
• Existing stabilization methods often struggle with complex delay dependencies and require difficult common Lyapunov function (CLF) analysis.
• The need for robust controllers that guarantee stability under arbitrary switching is critical.

Purpose of the Study:

• To develop a novel pole assignment stabilization strategy for switched nonlinear time-varying delay systems.
• To address more general time-varying delays that are dependent on the subsystem number.
• To propose a design that circumvents the complex search for common Lyapunov functions.

Main Methods:

• Utilized memory state feedback controllers for system stabilization.
• Employed novel common Lyapunov functions (CLFs) in conjunction with aggregation techniques.
• Applied the properties of these functions and the Borne-Gentina criterion to establish new algebraic stabilization criteria.

Main Results:

• New algebraic stabilization criteria were successfully established for the considered class of systems.
• The proposed controller design guarantees the stability of the closed-loop systems even under arbitrary switching.
• Effectiveness demonstrated through four illustrative examples, confirming the practical applicability of the method.

Conclusions:

• The developed method provides an effective approach for stabilizing switched nonlinear time-varying delay systems.
• The technique successfully avoids the computationally intensive search for common Lyapunov functions.
• The results offer a valuable contribution to the field of robust control for complex dynamical systems.