THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS

2002 ◽  
Vol 12 (06) ◽  
pp. 1371-1384 ◽  
Author(s):  
HENDRIK RICHTER
Keyword(s):  
Discrete Time ◽  
Finite Dimension ◽  
Initial Conditions ◽  
Henon Maps ◽  
Hénon Maps ◽  
Discrete Time Systems ◽  
Higher Dimensional ◽  
Parameter Values ◽  
Time Systems

The generalized Hénon maps (GHM) are discrete-time systems with given finite dimension, which show chaotic and hyperchaotic behavior for certain parameter values and initial conditions. A study of these maps is given where particularly higher-dimensional cases are considered.

scholarly journals STABILIZATION OF UNSTABLE PERIODIC ORBITS FOR DISCRETE TIME CHAOTIC SYSTEMS BY USING PERIODIC FEEDBACK

2006 ◽  
Vol 16 (02) ◽  
pp. 311-323 ◽  
Author(s):  
ÖMER MORGÜL
Keyword(s):  
Periodic Orbits ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Unstable Periodic Orbits ◽  
Discrete Time Systems ◽  
Feedback Scheme ◽  
Higher Dimensional ◽  
Periodic Feedback ◽  
Time Systems ◽  
Stability Results

We propose a periodic feedback scheme for the stabilization of periodic orbits for discrete time chaotic systems. We first consider one-dimensional discrete time systems and obtain some stability results. Then we extend these results to higher dimensional discrete time systems. The proposed scheme is quite simple and we show that any hyperbolic periodic orbit can be stabilized with this scheme. We also present some simulation results.

scholarly journals Robust Local Stabilization of Discrete-Time Systems with Time-Varying State Delay and Saturating Actuators

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
J. V. V. Silva ◽  
L. F. P. Silva ◽  
I. Rubio Scola ◽  
V. J. S. Leite
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Control Law ◽  
Time Varying ◽  
Region Of Attraction ◽  
Synthesis Conditions ◽  
Saturating Actuators ◽  
Discrete Time Systems ◽  
Time Systems

The robust local stabilization of uncertain discrete-time systems with time-varying state delayed and subject to saturating actuators is investigated in this work. A convex optimization method is proposed to compute robust state feedback control law such that the uncertain closed-loop is locally asymptotically stable if the initial condition belongs to an estimate of the region of attraction for the origin. The proposed procedure allows computing estimates of the region of attraction through the intersection of ellipsoidal sets in an augmented space, reducing the conservatism of the estimates found in the literature. Also, the conditions can handle the amount of delay variation between two consecutive samples, which is new in the literature for the discrete-time case. Although the given synthesis conditions are delay dependent, the proposed control law is delay independent, yielding to easier real time implementations. A convex procedure is proposed to maximize the size of the set of safe initial conditions. Numerical examples are provided to illustrate the effectiveness of our approach and also to compare it with other conditions in the literature.

scholarly journals Local Stabilization of Time-Delay Nonlinear Discrete-Time Systems Using Takagi-Sugeno Models and Convex Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Luís F. P. Silva ◽  
Valter J. S. Leite ◽  
Eugênio B. Castelan ◽  
Michael Klug
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Cartesian Product ◽  
Fuzzy Model ◽  
Convex Programming Problem ◽  
Discrete Time Systems ◽  
K Function ◽  
Takagi Sugeno ◽  
Time Systems ◽  
Fuzzy State

A convex condition in terms of linear matrix inequalities (LMIs) is developed for the synthesis of stabilizing fuzzy state feedback controllers for nonlinear discrete-time systems with time-varying delays. A Takagi-Sugeno (T-S) fuzzy model is used to represent exactly the nonlinear system in a restricted domain of the state space, called region of validity. The proposed stabilization condition is based on a Lyapunov-Krasovskii (L-K) function and it takes into account the region of validity to determine a set of initial conditions for which the actual closed-loop system trajectories are asymptotically stable and do not evolve outside the region of validity. This set of allowable initial conditions is determined from the level set associated to a fuzzy L-K function as a Cartesian product of two subsets: one characterizing the set of states at the initial instant and another for the delayed state sequence necessary to characterize the initial conditions. Finally, we propose a convex programming problem to design a fuzzy controller that maximizes the set of initial conditions taking into account the shape of the region of validity of the T-S fuzzy model. Numerical simulations are given to illustrate this proposal.

scholarly journals Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

2013 ◽  
Vol 23 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
The State ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

Sign in / Sign up

Export Citation Format

Share Document