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

• Published in: Automatica (Oxford) 1999, Vol.35 (2), p.259-268
• Main Authors: Costa, O.L.V., do Val, J.B.R., Geromel, J.C.
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Convex programming; Exact sciences and technology; Jump process; Linear systems; Markov parameters; Parameter uncertainty; Quadratic control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/S0005-1098(98)00145-9

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 Π=[ π ij ] for the Markov chain may not be exactly known, but belongs to an appropriate convex set. An equivalence between the convex formulation when Π 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.