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Switching Stabilization of Continuous-Time Switched Systems

Lu, Yueyun
http://orcid.org/0000-0002-5052-5679
http://rave.ohiolink.edu/etdc/view?acc_num=osu1479201964449478

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
This thesis develops a framework to study switching stabilization problems of continuous-time switched systems. Four types of switching stabilizability are formalized under different assumptions on the switching control input and adopted solution notions. On the time-domain, we define switching stabilizability as the existence of a measurable switching signal under which the resulting time-varying system is asymptotically stable. Discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length. On the state-feedback side, we define feedback stabilizability in Filippov sense (respectively, sample-and-hold sense) as the existence of a feedback law under which closed-loop Filippov solution (respectively, sample-and-hold solution) is asymptotically stable. The study on switching stabilization is divided into the special switched linear system case and the general case. For switched linear systems, it is proved that the four switching stabilizability notions are equivalent and their sufficient and necessary condition is the existence of a piecewise quadratic control-Lyapunov function that can be expressed as the pointwise minimum of a finite number of quadratic functions. For the general switched nonlinear systems, we focus on the notion of feedback stabilizability in Filippov sense. A piecewise smooth control-Lyapunov function framework is developed for constructive design of switching laws and stability guarantee for sliding motions. We discuss various technical issues emerging from nonsmooth surfaces of control-Lyapunov function and discontinuous surfaces of vector field. Sufficient conditions are derived for closed-loop stability including sliding motions on the attractive sliding surfaces.
Wei Zhang (Advisor)
Andrea Serrani (Committee Member)
Vadim Utkin (Committee Member)
105 p.
Electrical Engineering
switched systems; switching stabilization; control-Lyapunov function; sliding motion; Filippov solution

Recommended Citations

Citations

  • Lu, Y. (2016). Switching Stabilization of Continuous-Time Switched Systems [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1479201964449478

    APA Style (7th edition)

  • Lu, Yueyun. Switching Stabilization of Continuous-Time Switched Systems. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1479201964449478.

    MLA Style (8th edition)

  • Lu, Yueyun. "Switching Stabilization of Continuous-Time Switched Systems." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1479201964449478

    Chicago Manual of Style (17th edition)

osu1479201964449478
646
© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.