Open AccessStability under events for a class of hybrid dynamical systems with continuous and discrete time variables
Author(s) -
Liu Bin,
Hill David J.
Publication year - 2019
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.2018.5180
Subject(s) - control theory (sociology) , mathematics , exponential stability , stability (learning theory) , dwell time , impulse (physics) , hybrid system , lyapunov function , event (particle physics) , discrete time and continuous time , dynamical systems theory , variable (mathematics) , class (philosophy) , computer science , statistics , mathematical analysis , control (management) , nonlinear system , artificial intelligence , medicine , clinical psychology , physics , quantum mechanics , machine learning
This studies the stability under events for a class of hybrid dynamical systems (HDSs). The HDS is modelled via continuous and discrete time (CDT) variables. It is allowed that an HDS has time‐varying, unstable, non‐linear, different dwell time, and infinite number of subsystems. The stability under events reflects the effects of switching and impulse type events in HDS. By defining the length of CDT variable and extending the notion of hybrid‐event‐time in the literature, the concepts on global uniform asymptotic stability (GUAS) and event‐GUAS are reasonably defined. By employing multiple Lyapunov‐like functions, criteria on GUAS and event‐GUAS are established. Moreover, by extending average dwell time (ADT) to hybrid ADT, the relations between GUAS and event‐GUAS are derived. And the criteria on global uniform exponential stability under events (event‐GUES) are obtained. A method via maximal admissible probabilities of unstable subsystems is proposed to test the conditions of event‐GUES. As two special cases, the traditional stability criteria of only continuous or discrete variables are also derived. Finally, three examples are provided to verify the main results.