Nonlinear systems and iterated function systems
نویسندگان
چکیده
Nonlinear systems, defined by a system of ODE’s, usually contain nonlinear terms. Under some circumstances these terms can be locally approximated by linear factors and by discretization can be transformed in the sequence of (hyperbolic) Iterated Function Systems (IFS). Then, this IFS generate a unique attractor that uses as a kind of characteristic set that reflects the dynamics in the vicinity of of the approximated point of the nonlinear system. M.S.C. 2000: 34A34, 28A80.
منابع مشابه
Rotation number and its properties for iterated function and non-autonomous systems
The main purpose of this paper is to introduce the rotation number for non-autonomous and iterated function systems. First, we define iterated function systems and the lift of these types of systems on the unit circle. In the following, we define the rotation number and investigate the conditions of existence and uniqueness of this number for our systems. Then, the notions rotational entropy an...
متن کاملConstruction of strict Lyapunov function for nonlinear parameterised perturbed systems
In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.
متن کاملImage Compression predicated on Recurrent Iterated Function Systems
Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting substantially of a vertical contraction factor function and nonlinear transformations. These RIFSs are applied to image compression.
متن کاملExtension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems
The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...
متن کاملA new approach based on state conversion to stability analysis and control design of switched nonlinear cascade systems
In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF ...
متن کامل