Stability Theory for Hybrid Dynamical Systems

2020 ◽  
pp. 1-6
Author(s):  
Andrew R. Teel
Keyword(s):  
Dynamical Systems ◽  
Stability Theory ◽  
Hybrid Dynamical Systems

Towards a stability theory of general hybrid dynamical systems

Automatica ◽  
1999 ◽  
Vol 35 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Anthony N. Michel ◽  
Bo Hu
Keyword(s):  
Dynamical Systems ◽  
Stability Theory ◽  
Hybrid Dynamical Systems

scholarly journals Stability theory for hybrid dynamical systems

1998 ◽  
Vol 43 (4) ◽  
pp. 461-474 ◽  
Author(s):  
Hui Ye ◽  
A.N. Michel ◽  
Ling Hou
Keyword(s):  
Dynamical Systems ◽  
Stability Theory ◽  
Hybrid Dynamical Systems

Well-posed hybrid systems and their properties

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Dynamical Systems ◽  
Hybrid Systems ◽  
Hybrid System ◽  
Stability Theory ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Hybrid Dynamical Systems ◽  
Uniqueness Of Solutions ◽  
Classical Setting ◽  
Well Posed

This chapter defines nominally well-posed hybrid systems and well-posed hybrid systems to be those hybrid systems, vaguely speaking, for which graphical limits of graphically convergent sequences of solutions, with no perturbations and with vanishing perturbations, respectively, are still solutions. In a classical setting, a well-posed problem is often defined as one in which a solution exists, is unique, and depends continuously on parameters. For hybrid dynamical systems, insisting on uniqueness of solutions and on their continuous dependence on initial conditions is very restrictive and, as it turns out, not necessary to develop a reasonable stability theory. In fact, stability theory results are possible for a quite general class of hybrid systems. The class of well-posed hybrid systems includes the Krasovskii regularization of a general hybrid system and, more generally, it includes every hybrid system meeting some mild regularity assumptions on the data.

Stability Theory of Dynamical Systems

1970 ◽  
Author(s):  
Nam Parshad Bhatia ◽  
George Philip Szegö
Keyword(s):  
Dynamical Systems ◽  
Stability Theory
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