Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps

The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2

Dissipativity Analysis and Synthesis for a Class of Nonlinear Stochastic Impulsive Systems

The dissipativity analysis and control problems for a class of nonlinear stochastic impulsive systems (NSISs) are studied. The systems are subject to the nonlinear disturbance, stochastic disturbance, and impulsive effects, which often exist in a wide variety of industrial processes and the sources of instability. Our aim is to analyse the dissipativity and to design the state-feedback controller and impulsive controller based on the dissipativity such that the nonlinear stochastic impulsive systems are stochastic stable and strictly (Q,S,R)-dissipative. The sufficient conditions are obtained in terms of linear matrix inequality (LMI), and a numerical example with simulation is given to show the correctness of the derived results and the effectiveness of the proposed method

Delay-dependent criterion for exponential stability analysis of neural networks with time-varying delays

This note investigates the problem of exponential stability of neural networks with time-varying delays. To derive a less conservative stability condition, a novel augmented Lyapunov-Krasovskii functional (LKF) which includes triple and quadruple-integral terms is employed. In order to reduce the complexity of the stability test, the convex combination method is utilized to derive an improved delay dependent stability criterion in the form of linear matrix inequalities (LMIs). The superiority of the proposed approach is demonstrated by two comparative examples