Vol. 9, No. 2, 2021

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Stabilization of bilinear switching control systems by a mode-dependent average dwell time strategy

Messaoud Touahria and Naceurdine Bensalem

Vol. 9 (2021), No. 2, 107–126
Abstract

In this paper, the stabilization problem for a class of hybrid systems is studied for the special case of “bilinear switching systems”, via a switching strategy called mode-dependent average dwell time, in which each subsystem has its own average dwell time and multiple Lyapunov function technique. Under this strategy of switching and this technique, we determine the state feedback control law and the time needed so that each subsystem keeps its stability and so the overall switching system stability. Therefore, our problem can be reformulated into linear matrix inequalities that can be solved numerically.

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Keywords
hybrid systems, bilinear systems, switched systems, stabilization, multiple Lyapunov functions, mode-dependent average dwell time
Mathematical Subject Classification
Primary: 34Dxx, 34Hxx, 34Mxx, 37Nxx, 93Dxx
Milestones
Received: 18 April 2020
Revised: 3 November 2020
Accepted: 28 January 2021
Published: 17 April 2021

Communicated by Emilio Barchiesi
Authors
Messaoud Touahria
Laboratory of Fundamental and Numerical Mathematics
Department of Mathematics
Faculty of Sciences
Ferhat Abbas Sétif University 1
Sétif
Algeria
Naceurdine Bensalem
Laboratory of Fundamental and Numerical Mathematics
Department of Mathematics
Faculty of Sciences
Ferhat Abbas Sétif University 1
Sétif
Algeria