Robust stability and robust stabilization of discrete-time linear stochastic systems

Vasile Drăgan (), Toader Morozan () and Adrian-Mihail Stoica
Additional contact information
Vasile Drăgan: Institute of Mathematics “Simion Stoilow” of the Romanian Academy
Toader Morozan: Institute of Mathematics “Simion Stoilow” of the Romanian Academy
Adrian-Mihail Stoica: University “Politehnica” of Bucharest, Faculty of Aerospace Engineering

Chapter 8 in Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems, 2010, pp 287-336 from Springer

Abstract: Abstract The main goal of this chapter is to investigate several aspects of the problem of robust stability and robust stabilization for a class of discrete-time linear stochastic systems subject to sequences of independent random perturbations and Markov jump perturbations. As a measure of the robustness of the stability of an equilibrium of a nominal system a concept of stability radius is introduced. A crucial role in determining the lower bound of the stability radius is played by the norm of a linear bounded operator associated with the given plant. This operator is called the input.output operator and it is introduced in Section 8.2. In Section 8.3 a stochastic version of the so-called bounded real lemma is proved. This result provides an estimation of the norm of the input.output operator in terms of the feasibility of some linear matrix inequalities (LMIs) or in terms of the existence of stabilizing solutions of a discrete-time generalized algebraic Riccati-type equation. In Section 8.4 the stochastic version of the so-called small gain theorem is proved. Then this result is used to derive a lower bound of robustness with respect to linear structured uncertainties. In the second part of this chapter we consider the robust stabilization problem of systems subject to both multiplicative white noise and Markovian jumps with respect to some classes of parametric uncertainty. Based on the bounded real lemma we obtain a set of necessary and sufficient conditions for the existence of a stabilizing feedback gain that ensures a prescribed level of attenuation of the exogenous disturbance. We also show that in the case of full state measurement if the disturbance attenuation problem has a solution in a dynamic controller form then the same problem is solvable via a control in a state feedback form. Finally a problem of H∞ filtering is solved.

Keywords: Exponential Stability; Robust Stability; Output Operator; Markovian Jump; Nominal System (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-0630-4_8

Ordering information: This item can be ordered from
http://www.springer.com/9781441906304

DOI: 10.1007/978-1-4419-0630-4_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().