Date: 19.04.2022

Time: 16:00 CEST (Central European Summer Time)

Title of the Talk: Dynamic Equations on Time Scales

Speaker: Dr. Vipin Kumar (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany)

Event  Link: Zoom

Abstract: In this seminar, we discuss the basics of time scales theory and the dynamic equations on time scales. More precisely, firstly we discuss some basic operators which are very important to study time scales calculus. We discuss the Hilger derivative or delta derivative followed by the delta integral. After that, we discuss the initial value problem on time scales and the variation of parameter formula. Furthermore, we also discuss the following research problem:
          Finite-Time Stability and Stabilization Results for Switched Impulsive Dynamical Systems on Time Scales:
Here, we study the finite-time stability (FTS) and finite time stabilization problems for a class of switched impulsive systems evolving on an arbitrary time domain. This problem is formulated using time scale theory where the time domain can be continuous, discrete, union of disjoint intervals with variable gaps and variable lengths or any combination of these. Using common Lyapunov-quadratic and Lyapunov-like functions, we establish sufficient conditions to ensure the FTS results. Further, to solve the stabilization problem, we design state feedback controllers. We have illustrated the effectiveness of the obtained analytical results though numerical examples.