Recursive algorithm based controller design for a class of discrete time chaotic systems

In this paper, stabilization problem of parametric strict feedback class of discrete time chaotic systems is addressed. The methodology followed here utilizes recursive procedure based on contraction framework and explicit structure of controller is derived for a class of nonlinear discrete time systems. Recursive design of controller using Lyapunov based analysis are well established but contraction theory based procedures are generally lacking. Effort is made to have a recursive algorithm for discrete time chaotic systems in contraction framework. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. Numerical simulations for three dimensional discrete time chaotic system are presented in the end to show the effectiveness of the proposed approach.