scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

01 Mar 2023-IEEE transactions on systems, man, and cybernetics (IEEE transactions on systems, man, and cybernetics)-Vol. 53, Iss: 3, pp 1573-1583
TL;DR: In this article , the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms.
Abstract: The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of $M$ -matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results.
References
More filters
BookDOI
01 Jan 2010

1,696 citations

Journal ArticleDOI
01 Jun 2010
TL;DR: To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree.
Abstract: This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.

982 citations

BookDOI
01 Jan 2011

914 citations

Book
10 May 2011
TL;DR: In this paper, the realization problem for positive fractional and continuous-discrete 2D linear systems with state-feedback was formulated and the stability analysis of fractional linear systems in frequency domain was studied.
Abstract: Fractional discrete-time linear systems.- Fractional continuous-time linear systems.- Fractional positive 2D linear systems.- Pointwise completeness and pointwise degeneracy of linear systems.- Pointwise completeness and pointwise degeneracy of linear systems with state-feedbacks.- Realization Problem for positive fractional and continuous-discrete 2D linear systems.- Cone discrete-time and continuous-time linear systems.- Stability of positive fractional 1D and 2D linear systems.- Stability analysis of fractional linear systems in frequency domain.- Stabilization of positive and fractional linear systems.- Singular fractional linear systems.- Positive continuous-discrete linear systems.- Laplace transforms of continuous-time functions and z-transforms of discrete-time functions. "/b>

615 citations

Journal ArticleDOI
TL;DR: The paper presents two new lemmas related to the Caputo fractional derivatives and a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems and is applied to the stability analysis of two Fractional Order Model Reference Adaptive Control schemes.

538 citations