NDLI: On the Robust Stability, Stabilization, and Stability Radii of Continuous-Time Infinite Markov Jump Linear Systems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Todorov, Marcos G. Fragoso, Marcelo D.
Copyright Year	2011
Abstract	This paper addresses the robust stochastic stability and stabilization of continuous-time Markov jump linear systems (MJLS), with the Markov jump parameters taking values in a countably infinite set. It is assumed that the state and input matrices are subjected to norm-bounded uncertainty with a prespecified structure, which encompasses the block-diagonal setting. We introduce new robust analysis and synthesis characterizations such that, unlike previous approaches in the MJLS literature, the scaling parameters are treated as decision variables in linear matrix inequalities. As a by-product, new contributions to the theory of stability radii of MJLS are provided. When restricted to the finite case, we further introduce new adjoint linear matrix inequality (LMI) characterizations for each of the robust analysis and synthesis problems, as well as for stability radii. Besides the interest in its own right, the adjoint approach allows us to verify that, in the general MJLS case, there is a gap between the complex stability radius and what can be assessed with scaled versions of the small-gain theorem. This suggests a fundamental limitation of the robustness against linear perturbations that the H$_\infty$ control of MJLS may provide. Some numerical examples, which include the robust control of two interconnected oscillators, illustrate the main results.
Starting Page	1171
Ending Page	1196
Page Count	26
File Format	PDF
ISSN	03630129
DOI	10.1137/090774410
e-ISSN	10957138
Issue Number	3
Volume Number	49
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-05-19
Access Restriction	Subscribed
Subject Keyword	Markov jump parameter Linear systems scaling Robust stability stability radii Continuous-time Markov processes on discrete state spaces robust control continuous-time linear systems Stabilization of systems by feedback
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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