Asynchronous control of discrete-time impulsive switched systems with mode-dependent average dwell time

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Discrete-time impulsive switched systems are crucial in various applications.
• Asynchronous control, where controller switching lags system mode switching, presents significant challenges.
• Existing methods often require strict synchronization, limiting practical implementation.

Purpose of the Study:

• To investigate the asynchronous control problem for discrete-time impulsive switched systems.
• To develop a stability analysis method that accommodates control-system asynchronism.
• To design a control law ensuring system stability despite switching delays.

Main Methods:

• Utilizing multiple Lyapunov functions (MLFs) for stability analysis.
• Employing a mode-dependent average dwell time (MDADT) technique to manage switching.
• Formulating stability and stabilization conditions using numerically feasible matrix inequalities.

Main Results:

• A looser asymptotic stability result for closed-loop systems is derived.
• The asynchronous control problem is effectively solved under a proposed switching law.
• The developed conditions are computationally tractable and validated by an example.

Conclusions:

• The proposed method provides a robust framework for asynchronous control of impulsive switched systems.
• The use of MLFs and MDADT offers improved stability analysis and control design.
• The numerical example confirms the practical effectiveness of the theoretical results.