Balanced truncation approach to model reduction of Markovian jump time-varying delay systems

This paper investigates the model reduction problem based on balanced truncation for uncertain continuous-time Markovian jump linear systems with time-varying delay in the states. Firstly, two generalized dissipation inequalities are proposed to find the positive matrices which could guarantee the stochastic stability of the original system. By simultaneously balancing these two positive matrices, we can obtain the balanced transformation matrix which balances the original system. Then the reduced order model can be derived by truncating the balanced model. In order to bound the reduced order error, we choose the reciprocally convex approach to deal with the delay term. Finally, an illustrative example is provided to show the effectiveness of the proposed new design techniques.