Constructive stability and stabilizability of positive linear discrete-time switching systems

TL;DR

This paper introduces a new class of positive linear discrete-time switching systems that allows for constructive analysis of stability and stabilizability, even with arbitrary component connections, enabling explicit trajectory construction.

Contribution

It defines a novel class of systems with constructive stability analysis that generalizes systems with independently switching components and supports arbitrary component connections.

Findings

Constructive methods for stability and stabilizability are applicable to the new class.

The class includes systems with arbitrarily connected components without losing resolvability.

Explicit construction of trajectories with extremal convergence rates is possible.

Abstract

We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. This class generalizes the class of systems with independently switching state vector components. The distinctive feature of this class is that, for any system from this class, its components or blocks can be arbitrarily connected in parallel or in series without loss of the `constructive resolvability' property. It is shown also that, for such systems, it is possible to build constructively the individual positive trajectories with the greatest or the lowest rate of convergence to the zero.