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Stability analysis of linear control systems with uncertain parameters

Fang, Yuguang
http://rave.ohiolink.edu/etdc/view?acc_num=case1057598985

Abstract Details

1994, Doctor of Philosophy, Case Western Reserve University, Systems and Control Engineering.
In this dissertation, we study stochastic stability of linear systems whose parameters are randomly varying in a certain sense. In particular, we present a new approach to stochastic stability analysis of systems whose system structure is randomly changing among a finite set of possibilities which capture the abrupt changes in systems parameters or sudden failures of system components. These types of systems are referred to as jump linear systems with a finite state Markov chain form process. We first investigate the properties of various types of moment stability for stochastic jump linear systems, and use large deviation theory to study the relationship between "lower moment" stability and almost sure stability. In particular, we have proved that the region for δ-moment stability is monotonically increasing as δ is decreasing to zero and asymptotically converges to the region for almost sure stability. Roughly speaking, this is equivalent to saying that almost sure stability is equivalent to δ-moment stability for sufficiently small δ > 0. Furthermore, we prove that although the top δ-moment Lyapunov exponent is, in general, not differentiable at zero, it is differentiable at zero from the right and its right derivative at zero is equal to the top Lyapunov exponent. This answers a long standing question in this area. Based on this analysis, a new Lyapunov function is constructed to obtain a very general sufficient condition for almost sure stability, and this condition is also conjectured to be a necessary condition for almost sure stability. Moreover, a few new approaches for the study of almost sure stability are proposed and some easily-testable conditions for both moment stability and almost sure stability are obtained. Based on the results on almost sure stability and moment stability, the stochastic stabilization problem is also considered and a few future research topics are identified. This dissertation is the first research work in the current literature to use large deviation theory to study stochastic stability and further represents a systematic study of almost sure stability of jump linear systems with a finite state Markov chain form process. It is our high hope that this work will pave the way for further studies on the almost sure (sample path) stability for stochastic systems.
Kenneth Loparo (Advisor)
328 p.
Stability analysis; linear control systems; uncertain parameters

Recommended Citations

Citations

  • Fang, Y. (1994). Stability analysis of linear control systems with uncertain parameters [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1057598985

    APA Style (7th edition)

  • Fang, Yuguang. Stability analysis of linear control systems with uncertain parameters. 1994. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1057598985.

    MLA Style (8th edition)

  • Fang, Yuguang. "Stability analysis of linear control systems with uncertain parameters." Doctoral dissertation, Case Western Reserve University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=case1057598985

    Chicago Manual of Style (17th edition)

case1057598985
1,112
© 1994, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.