Basin, M.V., Gonzalez, J.R. and Fridman, L. (2003) Optimal and Robust Sliding Mode Control for Linear Systems with Time Delays in Control Input. International Journal of Pure and Applied Mathematics, 5, 395-420.

has been cited by the following article:

• TITLE: Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

  AUTHORS: Vishal Goyal, Vinay Kumar Deolia, Tripti Nath Sharma

  KEYWORDS: Discrete-Time Nonlinear Systems, Lyapunov-Krasovskii Functional, Linear Matrix Inequality (LMI), Sliding Mode Control (SMC), Chebyshev Neural Networks (CNNs)

  JOURNAL NAME: Intelligent Control and Automation, Vol.6 No.1, January 27, 2015

  ABSTRACT: This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.