Nonlinear H∞ control of stochastic time-delay systems with Markovian switching

In this paper, the stabilization and H∞ control problems are investigated for a class of stochastic time-delay systems with both nonlinear disturbances and Markovian jumping parameters. The purpose of the stochastic stabilization problem is to design a memoryless state feedback controller such that, for the addressed nonlinear disturbances as well as Markovian jumping parameters, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. In the H∞ control problem, in addition to the mean-square exponential stability requirement, a prescribed H∞ performance index is required to be achieved. By using Itô’s differential formula and the Lyapunov stability theory, sufficient conditions for the solvability of these problems are derived in term of linear matrix inequalities, which can be easily checked by resorting to available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed results.