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- R. Goebel
- 2005

Motivated by questions in stability theory for hybrid dynamical systems, we establish some fundamental properties of the set of solutions to such systems. Using the notion of a hybrid time domain and general results on set and graphical convergence, we establish under weak regularity and local boundedness assumptions that the set of solutions is… (More)

- R. Goebel
- 2007

Given a pair of convex conjugate functions f and f∗, we investigate the relationship between local Lipschitz continuity of ∇f and local strong convexity properties of f∗.

1066-033X/09/$25.00©2009IEEE Digital Object Identifier 10.1109/MCS.2008.931718 M any dynamical systems combine behaviors that are typical of continuous-time dynamical systems with behaviors that are typical of discrete-time dynamical systems. For example, in a switched electrical circuit, voltages and currents that change continuously according to classical… (More)

- Rafal Goebel
- 2007

It is shown that any convex function can be approximated by a family of differentiable with Lipschitz continuous gradient and strongly convex approximates in a “self-dual” way: the conjugate of each approximate is the approximate of the conjugate of the original function. The approximation technique extends to saddle functions, and is self-dual with respect… (More)

A continuous time infinite horizon linear quadratic regulator with input constraints is studied. On the theoretical side, optimality conditions, both in the open loop and feedback form, are shown together with smoothness of the value function and local Lipschitz continuity of the optimal feedback. Arguments are self-contained, use basic ideas of convex… (More)

In this paper we mainly consider the class LN of all locally nilpotent groups. Using similar arguments as in [GrS] we first show that there is no universal group in LNλ if λ is a cardinal such that λ = λ0 ; here we call a group G universal (in LNλ) if any group H ∈ LNλ can be embedded into G where LNλ denotes the class of all locally nilpotent groups of… (More)

We construct a continuous feedback for a saturated system ẋ(t) = Ax(t) + Bσ(u(t)). The feedback renders the system asymptotically stable on the whole set of states that can be driven to 0 with an open-loop control. Trajectories of the resulting closed-loop system are optimal for an auxiliary optimal control problem with a convex cost and linear dynamics.… (More)

- R. Göbel
- 1996

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer–Specker group Zא0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z.

- E. N. Barron, R. Goebel, R. R. Jensen
- SIAM Journal on Optimization
- 2012

We study a zero sum differential game under strong assumptions of convexity — the cost is convex for one player, and concave for the other. An explicit necessary and sufficient condition for a saddle point of the game is given in terms of convex analysis subgradients of the conjugate of the cost function. A generalized Hamiltonian equation is shown to… (More)

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