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Robust Stabilization of Linear Stochastic Systems

In: Mathematical Methods in Robust Control of Linear Stochastic Systems

Author

Listed:
  • 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)

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 $$\mathcal{D} =\{ 1,2,\ldots,d\}$$ .

Suggested Citation

  • Vasile Dragan & Toader Morozan & Adrian-Mihail Stoica, 2013. "Robust Stabilization of Linear Stochastic Systems," Springer Books, in: Mathematical Methods in Robust Control of Linear Stochastic Systems, edition 2, chapter 0, pages 381-436, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8663-3_9
    DOI: 10.1007/978-1-4614-8663-3_9
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