access icon free 2 control of discrete-time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi-simplex modelling

This study is concerned with the problem of ℋ2 state-feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the transition probability matrix is not precisely known, but belongs to a polytopic domain, or contains unknown or bounded elements. As a first contribution, the uncertainties of the transition probability matrix are modelled in terms of the Cartesian product of simplexes, called multi-simplex. Thanks to this representation, the problem of robust mean square stability analysis with an ℋ2 norm bound can be solved through convergent linear matrix inequality (LMI) relaxations constructed in terms of polynomial solutions. The proposed conditions yield a better trade-off between precision and computational effort when compared with other methods. As a second contribution, new conditions in terms of LMIs with a scalar parameter lying in the interval (− 1, 1) are proposed for ℋ2 state-feedback control with complete, partial or no observation of the Markov chain. Owing to the presence of the scalar parameter, less conservative results when compared with other conditions available in the literature can be obtained, at the price of increasing the associated computational effort. Numerical examples illustrate the advantages of the proposed methodology.

Inspec keywords: mean square error methods; Markov processes; state feedback; linear matrix inequalities; H2 control; discrete time systems; stability; control system synthesis; uncertain systems; linear systems

Other keywords: polytopic domain; MJLS; convergent linear matrix inequality relaxations; polynomial solutions; state-feedback control design; precision effort; Cartesian product; scalar parameter; multisimplex modelling; computational effort; LMI; robust mean square stability analysis; uncertain transition probability matrix; discrete-time Markov jump linear systems; â„‹2 control

Subjects: Discrete control systems; Linear algebra (numerical analysis); Stability in control theory; Control system analysis and synthesis methods; Markov processes; Interpolation and function approximation (numerical analysis)

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An Erratum has been published for this content:
Addendum to ‘ H 2 control of discrete-time Markov jump linear systems with uncertain transition probability matrix: improved LMI relaxations and multi-simplex modeling’