Abstract
This paper discusses about the stabilization of unknown nonlinear discrete-time fixed state delay systems. The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is presented for approximating the system nonlinearity. Using appropriate Lyapunov-Krasovskii functional the stability of the nonlinear system is ensured by the solution of linear matrix inequalities. Finally, a relevant example is given to illustrate the effectiveness of the proposed control scheme.
Highlights
Over the past few decades, time-delay systems have drawn much attention from researchers throughout the world
The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is presented for approximating the system nonlinearity
Using appropriate Lyapunov-Krasovskii functional the stability of the nonlinear system is ensured by the solution of linear matrix inequalities
Summary
Over the past few decades, time-delay systems have drawn much attention from researchers throughout the world. In [21] problem of feedback stabilization of nonlinear discrete-time systems with delays is explained. In this by using the Lyapunov-Razumikhin approach, general conditions for stabilizing the closed-loop system is derived. An optimal control scheme for a class of discrete-time nonlinear systems with time delays in both state and control variables with respect to a quadratic performance index function using adaptive dynamic programming is presented in [24]. Upper subscript T is the transpose of matrix and the symmetric entries in a symmetric matrix are given by *
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