Exponential dissipativeness of the random-structure diffusion processes and problems of robust stabilization. (English. Russian original) Zbl 1146.93038
Autom. Remote Control 68, No. 10, 1852-1870 (2007); translation from Avtom. Telemekh. 2007, No. 10, 134-154 (2007).
Summary: Consideration was given to the class of systems described by a finite set of the controllable control-affine diffusion Itô processes with stepwise transitions defined by the evolution of the uniform Markov chain (Markov switchings). For these systems, the notion of exponential dissipativity was introduced, and its theory was developed and used to estimate the possible variations of the output feedback law under which the system retains its robust stability. For the set of linear systems with uncertain parameters, there was proposed a two-step procedure to determine the output feedback control based on comparison with the stochastic model and providing their simultaneous robust stabilization. At the first step, the robust stabilizing control is established by means of an iterative algorithm. Then, the possible variations of the feedback law for which the robust stability is retained are estimated by solving a system of matrix linear inequalities. An example was presented.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
| 93B52 | Feedback control |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
controllable control-affine diffusion Itô processes; Markov chain; exponential dissipativity; output feedback controlReferences:
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