Abstract
This paper considers the problem of uniformly asymptotic stability (UAS) for discrete-time switched linear time-varying (DSLTV) systems. Starting with discrete-time linear time-varying (DLTV) systems, some stability conditions are given by using function-dependent linear matrix inequalities (LMIs). Comparing with the existing results, the conditions obtained allow the norm and rate of variation of system matrix are unbounded. Furthermore, the obtained results are extended to study the UAS of DSLTV systems, the stability condition is given by combining the methods of function-dependent LMIs with average dwell time. Finally, some further discussions about the relaxation of conditions obtained are also proposed. Three numerical examples are given to illustrate the theoretical results.
Highlights
As a class of important hybrid systems, switched systems have drawn considerable attentions and interests in control field due to their significance in both theory and applications
This approach is quite effective for studying discrete-time switched linear time-invariant (DSLTI) systems [5], [13]–[22]
It is noticing that these linear matrix inequalities (LMIs) method may not be readily applied to discrete-time switched linear time-varying (DSLTV) systems due to the
Summary
As a class of important hybrid systems, switched systems have drawn considerable attentions and interests in control field due to their significance in both theory and applications. To study the stability of discrete-time switched systems, researchers proposed many effective approaches, and one of them is the technique of LMIs based on Lyapu-nov stability theory. These requirements restrict the practical applications and theoretical research of DLTV systems They are the realistic and challenging problems that how to relax these restrictions and extend the obtained results to the case of DSLTV systems. It is noticing that the main technical difficulty for studying the stability for DSLTV based on functiondependent LMIs include the following two aspects: 1) the conventional LMIs method can be used to analyze the stability of DSLTI systems, but it can not be used to analyze the stability of DSLTV ones, or the result obtained is conservative. The main contributions of this paper include: i) two stability conditions are proposed for DLTV systems by using function-dependent LMIs (Compa-ring with the existing results, the conditions obtained allow the norm and rate of variation of system matrix are unbounded), ii) the stability condition is given for DSLTV systems by combining the methods of function-dependent LMIs with average dwell time, iii) some further discussions and two relaxed stability conditions that allows all subsystems are unstable are given
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.
