Wandering Intervals for Lorenz Maps with Bounded Nonlinearity

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

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New stability conditions for a class of nonlinear discrete-time systems with time-varying delay

10.36227/techrxiv.14152046.v1 ◽

2021 ◽

Author(s):

SAMI ELMADSSIA ◽

KARIM SADAAOUI

Keyword(s):

Discrete Time ◽

Stability Conditions ◽

Time Varying ◽

Time Varying Delay ◽

Discrete Time Systems ◽

Matrix Properties ◽

Arrow Form Matrix ◽

Bounded Nonlinearity ◽

Time Systems ◽

Varying Delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

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On α-Limit Sets in Lorenz Maps

Entropy ◽

10.3390/e23091153 ◽

2021 ◽

Vol 23 (9) ◽

pp. 1153

Author(s):

Łukasz Cholewa ◽

Piotr Oprocha

Keyword(s):

Topological Entropy ◽

Dynamical Behavior ◽

Unimodal Maps ◽

Limit Sets ◽

Lorenz Maps ◽

Provided Examples

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how the performed study on the structure of α-limit sets is closely connected with the calculation of the topological entropy.

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Experimental and Simulated Chaotic RLD Circuit Analysis with the Use of Lorenz Maps

Chaos and Complex Systems ◽

10.1007/978-3-642-33914-1_56 ◽

2012 ◽

pp. 403-409 ◽

Cited By ~ 1

Author(s):

N. A. Gerodimos ◽

P. A. Daltzis ◽

M. P. Hanias ◽

H. E. Nistazakis ◽

G. S. Tombras

Keyword(s):

Circuit Analysis ◽

Lorenz Maps

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Topological properties of Lorenz maps derived from unimodal maps

The Journal of Difference Equations and Applications ◽

10.1080/10236198.2020.1760260 ◽

2020 ◽

Vol 26 (8) ◽

pp. 1174-1191 ◽

Cited By ~ 1

Author(s):

Ana Anušić ◽

Henk Bruin ◽

Jernej Činč

Keyword(s):

Topological Properties ◽

Unimodal Maps ◽

Lorenz Maps

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An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4005276 ◽

2011 ◽

Vol 134 (1) ◽

Cited By ~ 28

Author(s):

K. Ramakrishnan ◽

G. Ray

Keyword(s):

Stability Analysis ◽

Stability Criterion ◽

Time Derivative ◽

Neutral Type ◽

Linear Matrix ◽

Lur’E Systems ◽

The Stability ◽

Delay Dependent ◽

Bounded Nonlinearity ◽

Delay Dependent Stability

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

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