Pareto-optimal solutions for Markov jump stochastic systems with delay

Pareto-optimal solutions for a class of general class of stochastic systems with both Markovian jumping parameters and time-delay are studied by introducing a linear matrix inequality (LMI) approach. In order to obtain a strategy set, new cross-coupled stochastic algebraic equations (CSAEs) are derived based on Karush-Kuhn-Tucker (KKT) conditions as necessary conditions. Furthermore, it is shown that the state feedback strategies can be obtained by solving LMIs. Finally, a numerical example is detailed that shows the effectiveness of the proposed methods.