No abstract

A class of super-linear stochastic delay differential equations (SDDEs) with variable delay and Markovian switching is considered. The main aim of this paper is to investigate the convergence and stability properties of partially truncated Euler-Maruyama (EM) method applied to the SDDEs with variable delay and Markovian switching under the generalized Khasminskii-type condition.

Summary In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.

SummaryIn this article, the problem of reduced‐order observer‐based controller design for a class of nonlinear time‐delay systems is addressed. First, we present sufficient conditions for the existence of the reduced‐order observer of nonlinear time‐delay systems. Then, a state feedback controller is designed to stabilize the systems. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the reduced‐order observer‐based controller. When the nonlinear part of systems satisfies the quasi‐one‐sided Lipschitz condition, the reduced‐order observer and feedback controller can be designed separately even though the parameter (A, C) of systems is not detectable and parameter (A, B) is not stabilizable. Finally, a numerical example is presented to show the effectiveness of the proposed approach.

This paper is concerned with a linear time-delay circuit and its feedback control. We use electronic components such as resistors and capacitors to realize a linear time-delay system. The time-delays are generated by operational amplifiers and single-chip microcomputers. Based on the actual data measured by the oscilloscope, the parameters of the system are estimated using the least square method. Then a comparison study between the waveform image measured by the oscilloscope and the numerical simulation obtained by MATLAB verifies the effectiveness of the parameters estimations of the circuit system. Furthermore, the circuit system is unstable with a large time-delay, a feedback controller is designed to stabilize the circuit system using the optimization method in the literature. Finally, the experimental results in the linear time-delay circuit show the effectiveness of the optimization method.