scholarly journals Robust dissipativity for uncertain impulsive dynamical systems

2003 ◽  
Vol 2003 (3) ◽  
pp. 119-128 ◽  
Author(s):  
Bin Liu ◽  
Xinzhi Liu ◽  
Xiaoxin Liao
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Supply Rate

We discuss the robust dissipativity with respect to the quadratic supply rate for uncertain impulsive dynamical systems. By employing the Hamilton-Jacobi inequality approach, some sufficient conditions of robust dissipativity for this kind of system are established. Finally, we specialize the obtained results to the case of uncertain linear impulsive dynamical systems.

scholarly journals Ruelle operator theorem for non-expansive systems

2009 ◽  
Vol 30 (2) ◽  
pp. 469-487 ◽  
Author(s):  
YUNPING JIANG ◽  
YUAN-LING YE
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Iterated Function Systems ◽  
Ruelle Operator ◽  
Iterated Function

AbstractThe Ruelle operator theorem has been studied extensively both in dynamical systems and iterated function systems. In this paper we study the Ruelle operator theorem for non-expansive systems. Our theorems give some sufficient conditions for the Ruelle operator theorem to be held for a non-expansive system.

On the Almost Sure Stability of Linear Stochastic Distributed-Parameter Dynamical Systems

1966 ◽  
Vol 33 (1) ◽  
pp. 182-186 ◽  
Author(s):  
P. K. C. Wang
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Integral Equations ◽  
Sufficient Conditions ◽  
Distributed Parameter ◽  
Almost Sure Stability ◽  
Partial Differential ◽  
Stochastic Parameters

In this paper, sufficient conditions for almost sure stability and asymptotic stability of certain classes of linear stochastic distributed-parameter dynamical systems are derived. These systems are described by a set of linear partial differential or differential-integral equations with stochastic parameters. Various examples are given to illustrate the application of the main results.

Large-Scale Impulsive Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Functions ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Supply Rate ◽  
Nonlinear Dynamical ◽  
Dissipation Inequality ◽  
Vector Lyapunov Functions ◽  
Definition Of ◽  
Stability Results

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.

Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems

1991 ◽  
Vol 43 (5) ◽  
pp. 1098-1120 ◽  
Author(s):  
Jianhong Wu ◽  
H. I. Freedman
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Stability And Convergence ◽  
Strong Monotonicity ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential ◽  
Monotone Dynamical Systems

AbstractThis paper is devoted to the machinery necessary to apply the general theory of monotone dynamical systems to neutral functional differential equations. We introduce an ordering structure for the phase space, investigate its compatibility with the usual uniform convergence topology, and develop several sufficient conditions of strong monotonicity of the solution semiflows to neutral equations. By applying some general results due to Hirsch and Matano for monotone dynamical systems to neutral equations, we establish several (generic) convergence results and an equivalence theorem of the order stability and convergence of precompact orbits. These results are applied to show that each orbit of a closed biological compartmental system is convergent to a single equilibrium.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

scholarly journals Surjunctivity and topological rigidity of algebraic dynamical systems

2017 ◽  
Vol 39 (3) ◽  
pp. 604-619 ◽  
Author(s):  
SIDDHARTHA BHATTACHARYA ◽  
TULLIO CECCHERINI-SILBERSTEIN ◽  
MICHEL COORNAERT
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Countable Group ◽  
Continuous Group ◽  
Continuous Map ◽  
Algebraic Dynamical Systems ◽  
Metrizable Group ◽  
Group Automorphisms

Let$X$be a compact metrizable group and let$\unicode[STIX]{x1D6E4}$be a countable group acting on$X$by continuous group automorphisms. We give sufficient conditions under which the dynamical system$(X,\unicode[STIX]{x1D6E4})$is surjunctive, i.e. every injective continuous map$\unicode[STIX]{x1D70F}:X\rightarrow X$commuting with the action of$\unicode[STIX]{x1D6E4}$is surjective.

scholarly journals Integrability of continuous bundles

2019 ◽  
Vol 2019 (752) ◽  
pp. 229-264 ◽  
Author(s):  
Stefano Luzzatto ◽  
Sina Tureli ◽  
Khadim War
Keyword(s):  
Dynamical Systems ◽  
Stable Manifold ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Classical Theorem ◽  
Uniqueness Of Solutions ◽  
Stable Manifold Theorem ◽  
New Criteria

Abstract We give new sufficient conditions for the integrability and unique integrability of continuous tangent subbundles on manifolds of arbitrary dimension, generalizing Frobenius’ classical theorem for {C^{1}} subbundles. Using these conditions, we derive new criteria for uniqueness of solutions to ODEs and PDEs and for the integrability of invariant bundles in dynamical systems. In particular, we give a novel proof of the Stable Manifold Theorem and prove some integrability results for dynamically defined dominated splittings.

scholarly journals Generalized Projective Synchronization for Different Hyperchaotic Dynamical Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. M. El-Dessoky ◽  
E. Saleh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lorenz System ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Hyperchaotic Lorenz System ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems

Projective synchronization and generalized projective synchronization have recently been observed in the coupled hyperchaotic systems. In this paper a generalized projective synchronization technique is applied in the hyperchaotic Lorenz system and the hyperchaotic Lü. The sufficient conditions for achieving projective synchronization of two different hyperchaotic systems are derived. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.

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