Impulse differential inclusions: a viability approach to hybrid systems

By J. Aubin, John Lygeros, M. Quincampoix, S. Sastry, N. Seube. IEEE Transactions on Automatic Control, 2002

321 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/19aef0e5543e32f1ebca22bca2175cb90f1eb730

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In Control and Systems Engineering

Citations in the corpus

Solutions to hybrid inclusions via set and graphical convergence with stability theory applications (2006, background): “In a slightly difierent setting, most of them were stated in [ 5 ]; we include them for completeness of presentation; the proof is in the Appendix.”
Hamilton–Jacobi Formulation for Reach–Avoid Differential Games (2009, methodology): “Following the same approach, the authors of [13] and [14] formulated viability, invariance, and pursuit-evasion gaming problems for hybrid systems and used nonsmooth analysis tools to characterize their solutions.”
Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle (2004, background): “, [11], [13]–[15]) but this simple one is sufficient for our purposes.”
On hybrid impulsive and switching systems and application to nonlinear control (2005, background): “Most recently, on the basis of Lyapunov functions and other analysis tools, the stability and stabilization for linear or nonlinear switched systems have been further investigated and many valuable results have been obtained, see [1], [4], [6], [7], [11], [15], [19], [22], and some references therei”
On reachability and minimum cost optimal control (2004, background): “Viability theory methods [8] have recently been extended from continuous systems to a broad class of hybrid systems known as impulse differential inclusions [41].”
Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability (2007, background): “[7], and van der Schaft and Schumacher [8].”
Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models (2011, methodology): “Similar to the viability kernel and the viable-capture basin (Aubin et al. 2002), we define an N-step viablecapture basin as the set of all N-step capturable states.”
Dynamical properties of hybrid automata (2003, background): “The hybrid automata considered here are a special case of the hybrid automata of [27] and the impulse differential inclusions of [28], both of which allow differential”
Hybrid systems: Generalized solutions and robust stability (2004, background): “See, for example, (Tavernini, 1987), (Michel and Hu, 1999), (Lygeros et al., 1999), (van der Schaft and Schumacher, 2000), (Aubin et al., 2002), and (Prieur, 2003).”