On the linear quadratic problem for systems with time reversed Markov jump parameters and the duality with filtering of Markov jump linear systems

摘要

We study a class of systems whose parameters are driven by a Markov chain inreverse time. A recursive characterization for the second moment matrix, aspectral radius test for mean square stability and the formulas for optimalcontrol are given. Our results are determining for the question: is it possibleto extend the classical duality between filtering and control of linear systems(whose matrices are transposed in the dual problem) by simply adding the jumpvariable of a Markov jump linear system. The answer is positive provided thejump process is reversed in time.