Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov-Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

Static output feedback frequency stabilization of time-delay power systems with coordinated electric vehicles state of charge control

In this paper, for the first time, electric vehicles are used for both the primary and secondary frequency controls to support power plants to rapidly suppress fluctuations in the system frequency due to load disturbances. Via networked control and wide-area communication infrastructures, multiple interval time-varying delays exist in the communication channels between the control center, power plant, and an aggregation of electric vehicles. By coordinating batteries’ state of charge control, the behaviors of the vehicle owners and the uncertainties imposed by the changes of the batteries’ state of charge are taken intoconsideration. A power system model incorporating multiple time-varying delays and uncertainties is first proposed. Then, a robust static output feedback frequency controller is designed to guarantee the resulting closed-loop system stable with an H∞ attenuation level. By utilizing a novel integral inequality, namely refined-Jensen inequality, and an improved reciprocally convex combination, the design conditions are formulated in terms of tractable linear matrix inequalities which can be efficiently solved by various computational tools. The effectiveness of the proposed control scheme is verified by extensive simulations.