Almost Sure Stability and Stabilization of Composite Switched Systems With Persistent Dwell Time Constraint

Area of Science:

• Control Systems Engineering
• Dynamical Systems Theory
• Stochastic Systems

Background:

• Composite switched systems (CSSs) present challenges in stability analysis due to complex switching behaviors.
• Ensuring exponential almost sure (EAS) stability is crucial for reliable system performance.
• Existing methods often lack generality or are overly conservative.

Purpose of the Study:

• To develop a novel dual-switching mechanism for achieving EAS stability and stabilization in CSSs.
• To establish sufficient conditions for EAS stability under a combined persistent dwell time (PDT) and Markov process switching.
• To provide a more general and less conservative stability analysis framework for CSSs.

Main Methods:

• Development of a dual-switching mechanism integrating persistent dwell time (PDT) and Markov processes.
• Establishment of interrelations between parameters under PDT constraints to manage switching frequency.
• Derivation of sufficient conditions for EAS stability and stabilization based on the designed switching strategy.

Main Results:

• Sufficient conditions for achieving exponential almost sure (EAS) stability and stabilization of CSSs are established.
• The proposed dual-switching mechanism ensures switching frequency remains within permissible limits under PDT constraints.
• The developed theoretical results are demonstrated to be more general and less conservative than previous works.

Conclusions:

• The novel dual-switching mechanism effectively guarantees EAS stability and stabilization for CSSs.
• The established conditions offer a less conservative and more broadly applicable approach to CSS stability analysis.
• The findings are validated through three illustrative examples, confirming the theoretical advancements.