Open AccessNew conditions for finite‐time stability of impulsive dynamical systems via piecewise quadratic functions
Author(s) -
Ambrosino Roberto,
Ariola Marco,
Garone Emanuele,
Amato Francesco,
Tartaglione Gaetano
Publication year - 2022
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/cth2.12308
Subject(s) - piecewise , mathematics , stability (learning theory) , interval (graph theory) , control theory (sociology) , quadratic equation , bounded function , finite set , linear matrix inequality , dynamical systems theory , convex optimization , regular polygon , mathematical optimization , mathematical analysis , computer science , control (management) , physics , geometry , combinatorics , quantum mechanics , machine learning , artificial intelligence
In this paper, the use of time‐varying pi ecew ise quadratic functions is investigated to characterize the finite‐time stability of state‐dependent impulsive dynamical linear systems. Finite‐time stability defines the behavior of a dynamic system over a bounded time interval. More precisely, a system is said to be finite‐time stable if, given a set of initial conditions, its state vector does not exit a predefined domain for a certain finite interval of time. This paper presents new sufficient conditions for finite‐time stability based on time‐varying piecewise quadratic functions. These conditions can be reformulated as a set of Linear Matrix Inequalities that can be efficiently solved through convex optimization solvers. Different numerical analysis are included in order to prove that the presented conditions are able to improve the results presented so far in the literature.