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Relationships between Linear Dynamically Varying Systems and Jump Linear Systems
Authors:S. Bohacek  E. A. Jonckheere
Affiliation:(1) Department of Electrical and Computer Engineering, University of Delaware, Newark, 000, 19716-3130 Delaware, U.S.A.;(2) Department of Electrical Engineering Systems, University of Southern California, no Street, 000, California 90089-2563 Los Angeles, U.S.A.
Abstract:
The connection between linear dynamically varying (LDV) systems and jump linear (JL) systems is explored. LDV systems have been used to model the error in nonlinear tracking problems. Some nonlinear systems, for example Axiom A systems, admit Markov partitions and their dynamics can be quantized as Markov chains. In this case the tracking error can be approximated by a JL system. It is shown that (i) JL controllers for arbitrarily fine partitions exist if and only if the LDV controller exists; (ii) the JL controller stabilizes the nonlinear dynamical system; (iii) JL controllers provide approximations of the LDV controller. Finally, it is shown that this process is robust against such errors in the probability structure as the inaccurate assumption that an easily constructed partition is Markov.Date received: August 20, 2001. Date revised: June 5, 2003. This research was supported by National Science Foundation Grant ECS-98-02594.
Keywords:Linear parameter varying (LPV) systems  Linear dynamically varying (LDV) systems  Jump linear (JL) systems  Markov partitions
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