The authors consider the quadratic optimal control problem of discrete-time Markovian jump linear systems (MJLS). Different from the related literature [cf. O. L. V. Costa, J. B. R. do Val and J. C. Geromel, Int. J. Control 66, 557-579 (1997); M. V. Kothare, V. Balakrishnan and M. Morari, Automatica 32, No. 10, 1361-1379 (1996; Zbl 0897.93023)], the problem here is under constraints on the norm of the state and control variables as well as with some uncertainties on the transition probability matrix and initial state (belonging to appropriate convex sets). It is shown that the problem can be stated in terms of a linear matrix inequalities (LMI) optimization problem, and then, via using convex programming, approximation for the optimal solution of the problem can be well obtained.
Numerical examples show the effectiveness of the proposed method.