Robust Stabilization of Linear Stochastic Systems

Vasile Dragan, Toader Morozan and Adrian-Mihail Stoica
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Vasile Dragan: Institute of Mathematics of the Romanian Academy
Toader Morozan: Institute of Mathematics of the Romanian Academy
Adrian-Mihail Stoica: University Politechnica of Bucharest

Chapter Chapter 9 in Mathematical Methods in Robust Control of Linear Stochastic Systems, 2013, pp 381-436 from Springer

Abstract: Abstract In the present chapter we consider the robust stabilization problem of systems subject to both multiplicative white noise and to Markovian jumps with respect to some classes of parametric uncertainty. As it is already known, a wide variety of aspects of the robust stabilization problem can be embedded in a general disturbance attenuation problem (DAP) which extends the well-known H ∞ control problem in the case of deterministic invariant linear systems. A special attention will be paid in this chapter to the attenuation problem of exogenous perturbations with a specified level of attenuation. In the same time, some particular robust stabilization problems which solutions are derived using the results in the preceding chapter will be presented. The solution of the general attenuation problem will be given in terms of some linear matrix inequalities which provides necessary and sufficient solvability conditions. Throughout this chapter we assume that $$\mathcal{D} =\{ 1,2,\ldots,d\}$$ .

Keywords: Kalman Filter; State Feedback; Output Operator; State Feedback Control; Linear Stochastic System (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-8663-3_9

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DOI: 10.1007/978-1-4614-8663-3_9

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