Stability of switched block upper-triangular linear systems with switching delay: Application to large distributed systems

Motivated by the distributed control of fleets of identical linear subsystems, we consider the stability of block upper-triangular switched linear systems with switching delay, when switching between stable modes. Proving globally uniformly asymptotic stability (GUAS) of a switched block upper-triangular linear system can be reduced to proving GUAS for each of its block diagonal subsystems. We derive a scalable LMI-based test for GUAS under arbitrary switching, with complexity linearly dependent on the number of block diagonal elements of the system. If the system is not GUAS under arbitrary switching, we partition the state-space into regions in which switching will preserve GUAS despite a delay between the state measurements and switching time. Although we tailor these results to block upper-triangular switched linear systems, they are applicable to any switched linear system with switching delay. Two examples include control of a formation of identical vehicles under supervisory discrete control, and a switched linear system under remote control.