Boundedness control sets for linear systems on Lie groups

Control Systems on Lie Groups

Motion Control for Nonholonomic Systems on Matrix Lie Groups

Title of Dissertation: Motion Control for Nonholonomic Systems on Matrix Lie Groups Herbert Karl Struemper, Doctor of Philosophy, 1997 Dissertation directed by: Professor P. S. Krishnaprasad Department of Electrical Engineering In this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coor...

Equivalence of Control Systems with Linear Systems on Lie Groups and Homogeneous Spaces

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field...

Controllability of Linear Systems with inner derivation on Lie Groups

A vector eld on a connected Lie group is said to be linear if its ow is a one parameter group of automorphisms. A control-a ne system is linear if the drift is linear and the controlled vector elds right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector eld is inner....

Robust uniformly ultimate boundedness control for uncertain switched linear systems

In this paper, piecewise linear switched systems affected by both parameter variations and exterior disturbances are considered. The problem of synthesis of switching laws, which assure that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated. Given an uncertain switched linear system, we present a systema...