On the stability of coupled differential-difference systems with multiple time-varying delays: a positivity-based approach

Iuliis, Vittorio De; D’Innocenzo, Alessandro; Germani, Alfredo; Manes, Costanzo

doi:10.1109/cdc40024.2019.9028858

Cited by 3 publications

(1 citation statement)

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“…[25]), whose general idea is to associate to a given non positive system an augmented positive representation whose state (and output, if modelled) trajectories always dominate those of the original system. The method has been systematically implemented for a number of different classes of delay systems by means of the internally positive representation (IPR) technique, see [26][27][28][29][30][31], which allowed to export to non positive systems stability results that only hold for positive ones, although at the expense of introducing some conservatism.…”

Section: Stability Of Arbitrary Delay Systems Via Iprmentioning

confidence: 99%

Stability conditions for linear discrete‐time switched systems in block companion form

Iuliis

D’Innocenzo

Germani

et al. 2020

IET Control Theory & Appl

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Switched models whose dynamic matrices are in block companion form arise in theoretical and applicative problems such as representing switched ARX models in state-space form for control purposes. Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work, the authors study the arbitrary switching stability for some classes of block companion discrete-time switched systems. They start from the special case in which the first block-row is made of permutations of non-negative matrices, deriving a simple necessary and sufficient stability condition under arbitrary switching. The condition is computationally less demanding than the sufficient-only existence of a linear common Lyapunov function. Then, both non-negativity and combinatorial assumptions are dropped, at the expense of introducing conservatism. Some implications on the computation of the joint spectral radius for the aforementioned families of matrices are illustrated.

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