Abstract
This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.
Highlights
As a special class of hybrid dynamical systems, switched systems [1] are interestingly used amongst a variety of engineering domains chemical processes, automotive engine control and aircraft control, power systems, power electronics, traffic control, network communications, and many other fields [1,2,3].From a theoretical point of view, stability represents one of the most significant problems for switched systems
A novel robust asymptotic stability criterion for a class of discrete-time switched nonlinear systems with time varying delays and subject to polytopic uncertainties is established via constructing a new common Lyapunov functional [9], according to the vector norm notion [9,10,11,12,13, 27,28,29,30,31] and M - matrix properties [32]
We present our first result on robust stability analysis for system (1)
Summary
As a special class of hybrid dynamical systems, switched systems [1] are interestingly used amongst a variety of engineering domains chemical processes, automotive engine control and aircraft control, power systems, power electronics, traffic control, network communications, and many other fields [1,2,3]. A novel robust asymptotic stability criterion for a class of discrete-time switched nonlinear systems with time varying delays and subject to polytopic uncertainties is established via constructing a new common Lyapunov functional [9], according to the vector norm notion [9,10,11,12,13, 27,28,29,30,31] and M - matrix properties [32]. New stability conditions are obtained by transforming the considered systems representation under the arrow form matrix [29] and employing the discrete-time Borne and Gentina practical stability criterion [30, 31] These proposed results are generalized for a class of switched systems with multiple time varying delays. I [k1 k2] denotes the set of integers {k1, k1 + 1, k1 + 2, ..., k2} and In is the identity matrix with appropriate dimension
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
