Related papers: Derived control theorems for reductive groups

We prove that the derived categories for toric varieties have complete exceptional collections.

We prove that the set of limit groups is recursive, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (a la Long and Reid) is coherent and, furthermore,…

We introduce a method to deal with the data-driven control design of nonlinear systems. We derive conditions to design controllers via (approximate) nonlinearity cancellation. These conditions take the compact form of data-dependent…

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order…

One approach for feedback control using high dimensional and rich sensor measurements is to classify the measurement into one out of a finite set of situations, each situation corresponding to a (known) control action. This approach…

This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem…

We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…

The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup…

We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.

This paper presents an approach that employs log-linearization in Lie group theory and the Newton-Euler equations to derive exact linear error dynamics for a multi-rotor model, and applies this model with a novel log-linear dynamic…

We describe the derived category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2). Then, we give an application to the Euler-characteristic version of the Hall algebra of…

In reference [8] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good…

In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional…

Let $G$ be a 1-connected, almost-simple Lie group over a local field and $\mathcal{S}$ a subsemigroup of $G$ with non-empty interior. The action of the regular hyperbolic elements in the interior of $\mathcal{S}$ on the flag manifold $G/P$…

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. When the state space is a solvable connected Lie group, controllability of the linear system is assured if the ad-rank condition holds.

We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems…

We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the…

We study the controlled dynamics of the {\it ensembles of points} of a Riemannian manifold $M$. Parameterized ensemble of points of $M$ is the image of a continuous map $\gamma:\Theta \to M$, where $\Theta$ is a compact set of parameters.…

We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…