Open AccessOn robust stability of switched linear systems
Author(s) -
Son Nguyen Khoa,
Van Ngoc Le
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0144
Subject(s) - mathematics , linear system , affine transformation , control theory (sociology) , stability (learning theory) , quadratic equation , lyapunov function , stability theory , upper and lower bounds , radius , marginal stability , mathematical analysis , computer science , nonlinear system , pure mathematics , geometry , control (management) , physics , computer security , quantum mechanics , artificial intelligence , machine learning , mechanics , instability
In this study, the robust stability of continuous‐time switched linear systems is investigated under the assumptions that the matrices of the associated linear subsystems are subjected to affine perturbations. The notion of structured stability radius of a switched linear system which is asymptotically exponentially stable w.r.t. arbitrary switchings is introduced. Some lower bounds and upper bounds for estimating this radius are established, by using the system's common quadratic Lyapunov functions and via an approach based on solutions comparison principle. When the nominal switched system is of special structures (for instance when all matrices of subsystems are normal) the obtained bounds yield easily computable formulas for calculating or estimating the system's stability radius. Several examples are provided to illustrate the authors' approach.