An implicit systems characterization of a class of impulsive linear switched control processes. Part 1: Modeling. (February 2015)

• Record Type: Journal Article
• Authors: Bonilla, M.; Malabre, M.; Azhmyakov, V.
• Is Part Of: Nonlinear analysis. Volume 15(2015)
• Page Start: 157
• Page End: 170
• Publication Date: 2015-02
• Subjects: Piecewise linear dynamic systems -- Impulsive switched control strategies -- Implicit differential equations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2014.04.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Our paper focuses on a fundamental structural property associated with a family of linear switched control systems in the presence of impulsive dynamics. We consider dynamic processes governed by piecewise linear ODEs with controlled location transitions and describe the resulting system in a constructive form of an implicit dynamic system. The proposed algebraic-based modeling framework follows the celebrated behavioral approach (see Polderman and Willems (1998)) and makes it possible to apply to the switched dynamics some conventional techniques from the well-established time-invariant implicit systems theory. The analytic results of our paper constitute a formal theoretical extension of switched control systems methodology and can be used (as an auxiliary step) in a concrete control design procedure. In this first part, we consider modeling aspects.