Graph-Based Restricted and Arbitrary Switching for Switched Positive Systems via a Weak CLCLF.

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Discrete-time switched positive linear systems (SPLSs) with marginally stable subsystems present unique stability challenges.
• Ensuring asymptotic stability in such systems requires advanced analytical techniques that account for both system dynamics and switching behaviors.

Purpose of the Study:

• To investigate and establish conditions for the asymptotic stability of discrete-time switched positive linear systems (SPLSs) with marginally stable subsystems.
• To develop novel methods for analyzing stability under different types of switching signals.

Main Methods:

• Utilizing the weak common linear copositive Lyapunov function (weak CLCLF) approach.
• Combining switching properties with state component properties.
• Developing cycle-dependent joint path conditions using switching digraphs and state component digraphs for transfer-restricted switching.
• Constructing path conditions for designing switching schemes under time interval sequences.

Main Results:

• Novel cycle-dependent joint path conditions are proposed for transfer-restricted switching signals.
• Two types of path conditions are developed for designing switching schemes under time interval sequences.
• Necessary and sufficient conditions for asymptotic stability under arbitrary switching are established.

Conclusions:

• The proposed weak CLCLF approach effectively ensures the asymptotic stability of SPLSs with marginally stable subsystems.
• The developed conditions and methods provide a robust framework for analyzing and designing stable switched systems.
• The effectiveness of the presented methods is validated through three illustrative examples.