Stability of networked control systems: A Lyapunov-Krasovskii functional plus approach.

This paper is concerned with stability for networked control systems with a transmission delay and data packet dropouts. A hybrid model is formulated for the networked control systems to separate the constant delay and data packet dropouts, and a stability theorem is established for the hybrid model. Based on the stability theorem, a Lyapunov-Krasovskii functional plus (LKFP) approach is proposed to revolutionize the normal Lyapunov-Krasovskii functional approach. By fully employing the system information to construct an LKFP and by exploiting integral equations of the hybrid model to deal with the derivative of the LKFP, new stability results are obtained. Finally, numerical examples illustrate that the stability results are of less conservatism than some existing ones.

Improved delay-dependent stability result for neural networks with time-varying delays.

This paper is concerned with a new Lyapunov-Krasovskii functional (LKF) approach to the stability for neural networks with time-varying delays. The LKF has two features: First, it can make full use of the information of the activation function. Second, it employs the information of the maximal delayed state as well as the instant state and the delayed state. When estimating the derivative of the LKF we employ a new technique that has two characteristics: One is that Wirtinger-based integral inequality and an extended reciprocally convex inequality are jointly employed; the other is that the information of the activation function is used as much as we can. Based on Lyapunov stability theory, a new stability result is obtained. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones.

New delay-dependent stability criteria for neural networks with two additive time-varying delay components.

This brief is concerned with delay-dependent stability for neural networks with two additive time-varying delay components. By constructing a new Lyapunov functional and using a convex polyhedron method to estimate the derivative of the Lyapunov functional, some new delay-dependent stability criteria are derived. These stability criteria are less conservative than some existing ones. An example is given to demonstrate the less conservatism of the stability results.

Delay-dependent stability for recurrent neural networks with time-varying delays.

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.