Indefinite Linear Quadratic Optimal Control Problem for Continuous-time Linear Descriptor Markov Jump Systems

The indefinite linear quadratic (ILQ) optimal control problem for continuous-time descriptor Markov jump systems (DMJSs) is discussed in this work. Firstly, by using elementary linear algebra approach, the ILQ problem of DMJSs can be equivalent to standard LQ problem of Markov jump systems (MJSs) with some inequality and rank conditions. Then sufficient condition of the ILQ problem for DMJSs being solvable is obtained according to the LQ theory of MJSs, the optimal state feedback control is given, and the optimal cost value can be guaranteed to be nonnegative, moreover, the obtained optimal closed-loop system is stochastically admissible. Lastly, a numerical example is provided to verify the validity of the presented methods.