Brief Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis

Authors:
O. L. V. Costa;J. B. R. Do Val;J. C. Geromel
Affiliations:
Department of Electronic Engineering, University of Sao Paulo, 05508-900 - Sao Paulo-SP, Brazil;LAC-DT/Faculty of Electrical Engineering, UNICAMP, CP 6101, 13081-970-Campinas-SP, Brazil;LAC-DT/Faculty of Electrical Engineering, UNICAMP, CP 6101, 13081-970-Campinas-SP, Brazil
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

Continuous-time H"2-control problem for the class of linear systems with Markovian jumps (MJLS) using convex analysis is considered in this paper. The definition of the H"2-norm for continuous-time MJLS is presented and related to the appropriate observability and controllability Gramians. A convex programming formulation for the H"2-control problem of MJLS is developed. That enables us to tackle the optimization problem of MJLS under the assumption that the transition rate matrix @P=[@p"i"j] for the Markov chain may not be exactly known, but belongs to an appropriate convex set. An equivalence between the convex formulation when @P is exactly known and the usual dynamic programming approach of quadratic optimal control of MJLS is established. It is shown that there exists a solution for the convex programming problem if and only if there exists the mean-square stabilizing solution for a set of coupled algebraic Riccati equations. These results are compared with other related works in the current literature.