Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales. Issue 1 (January 2021)

• Record Type: Journal Article
• Authors: Kumar, Vipin; Djemai, Mohamed; Defoort, Michael; Malik, Muslim
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 1(2021)
• Page Start: 674
• Page End: 698
• Publication Date: 2021-01
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2020.11.001
• Languages: English
• ISSNs: 0016-0032

Abstract

Highlights: The results of this manuscript is on arbitrary time domain which are formulated in terms of time scales. It includes the continuous, discrete as well as any combination of these two, henceforth the results of this manuscript are non-trivial extension of the existing results. There are many applications which have some jumps at some specific time moments. So, we considered an impulsive switched system and established the finite time stability (FTS) results. To established these results, we constructed common Lypunov quadratic functions on time scales in which the delta derivative of these functions should be negative definite. In addition, we also established FTS re- sults by constructing some Lyapunov like functions on time scales in which we relax the condition of negative definiteness. Some numerical simulation for different time domains are given to verify the proposed theoretical results. Abstract: In this article, 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.