Results on relaxation theorems for hybrid systems (2008)
Chaohong Cai, Andrew R. Teel, Rafal Goebel
states that the solution set of a locally Lipschitz differential inclusion is dense in the solution set of its convexified differential inclusion in the uniform metric on compact time intervals. For...
Hybrid Systems Techniques for Convergence of Solutions to Switching Systems (2008)
Rafal Goebel, Ricardo G. Sanfelice, Andrew R. Teel
Invariance principles for hybrid systems are used to derive invariance principles for nonlinear switching systems with multiple Lyapunov-like functions. Dwell-time, persistent dwell-time, and weak...
Hybrid systems: Generalized solutions and robust stability (2004)
Rafal Goebel, Joao Hespanha, Andrew R. Teel, Chaohong Cai, Ricardo Sanfelice
Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that...
Stability regions for saturated linear systems via conjugate lyapunov functions (2004)
Tingshu Hu, Zongli Lin, Rafal Goebel, Andrew R. Teel
Abstract — We use a recently developed duality theory for linear differential inclusions (LDIs) to enhance the stability analysis of systems with saturation. Based on the duality theory, the...
Hybrid Systems: Generalized (2004)
Solutions And Robust, Rafal Goebel, Joao Hespanha, Andrew R. Teel, Chaohong Cai, Ricardo Sanfelice
Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an...
On the nondifferentiability of cone-monotone functions in Banach spaces (2002)
Borwein, Jonathan M., Goebel, Rafal
In finite-dimensional spaces, cone-monotone functions -- a special case of which are the coordinate-wise nondecreasing functions -- possess several regularity properties like almost everywhere...
Notions of Relative Interior in Banach Spaces (2001)
Borwein, Jonathan M., Goebel, Rafal
Extensions to a Banach space of the equivalent notions of relatively absorbing, non-support, and relative interior points of a convex set in $\reals^n$ are presented. The relations between these...
Convexity and Hamiltonian equations in differential games (1998)
We study a zero sum di#erential game under strong assumptions of convexity --- the cost is convex for one player, and concave for the other. An explicit necessary and su#cient condition for a saddle...