Total controllability results for a class of time‐varying switched dynamical systems with impulses on time scales

2020 ◽  
Author(s):  
Vipin Kumar ◽  
Mohamed Djemai ◽  
Michael Defoort ◽  
Muslim Malik
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Time Varying ◽  
Total Controllability

scholarly journals Matrix measures, stability and contraction theory for dynamical systems on time scales

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giovanni Russo ◽  
Fabian Wirth
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Upper Bound ◽  
Time Scale ◽  
Nonlinear Dynamical Systems ◽  
Linear Time ◽  
Sufficient Condition ◽  
Time Varying ◽  
Time Varying Systems ◽  
Matrix Measures

<p style='text-indent:20px;'>This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study both linear and nonlinear dynamical systems on time scales. Specifically, we start with considering linear time-varying systems and, for these, we prove a time scale analogous of an upper bound due to Coppel. We make use of this upper bound to give stability and input-to-state stability conditions for linear time-varying systems. Then, we consider nonlinear time-varying dynamical systems on time scales and establish a sufficient condition for the convergence of the solutions. Finally, after linking our results to the existence of a Lyapunov function, we make use of our approach to study certain epidemic dynamics and complex networks. For the former, we give a sufficient condition on the parameters of a SIQR model on time scales ensuring that its solutions converge to the disease-free solution. For the latter, we first give a sufficient condition for pinning synchronization of complex time scale networks and then use this condition to study certain collective opinion dynamics. The theoretical results are complemented with simulations.</p>

scholarly journals Controllability and observability of linear impulsive adjoint dynamic system on time scale

2020 ◽  
Vol 51 (3) ◽  
pp. 201-217
Author(s):  
Nusrat Yasmin ◽  
Safia Mirza ◽  
Awais Younus ◽  
Asif Mansoor
Keyword(s):  
Dynamic System ◽  
Time Scales ◽  
Time Scale ◽  
Continuous Case ◽  
Time Varying ◽  
Controllability And Observability

This paper deals with the controllability, observability of the solution of time-varying system on time scales. We obtain new results about controllability and observability and generalize to a time scale some known properties about stability from the continuous case.

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

A Wavelet Based Procedure to Study Vibrations and Stability

1999 ◽  
Author(s):  
S. Pernot ◽  
C. H. Lamarque
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Time Varying ◽  
Differential Systems ◽  
Varying Coefficients ◽  
Linear Differential Systems ◽  
Time Varying Coefficients ◽  
Linear Differential

Abstract A Wavelet-Galerkin procedure is introduced in order to obtain periodic solutions of multidegrees-of-freedom dynamical systems with periodic time-varying coefficients. The procedure is then used to study the vibrations of parametrically excited mechanical systems. As problems of stability analysis of nonlinear systems are often reduced after linearization to problems involving linear differential systems with time-varying coefficients, we demonstrate the method provides efficient practical computations of Floquet exponents and consequently allows to give estimators for stability/instability levels. A few academic examples illustrate the relevance of the method.

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