Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and It?o's differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.
The relationship between the technique by statedependent Riccati equations (SDRE) and Hamilton-Jacobi-Isaacs (HJI) equations for nonlinear H ∞ control design is investigated.By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices,a method is proposed for examining whether the SDRE method admits a global optimal control equivalent to that solved by the HJI equation method.Two examples with simulation are given to illustrate the method is effective.
