SYSTEM THEORY ON GROUP MANIFOLDS AND COSET SPACES

Author : Roger Ware Brockett

Presented by James Ladzekpo

Western Michigan University

INTRODUCTION

MOTIVATION

• The main motivation of this paper came from some work on Lie algebraic method in differential equations by W. Magnus, K. T Chen, J. Wei and E. Norman and above all, from being confronted with certain physical problems where linear theory was simply inadequate.

EXAMPLES

EXAMPLES

2. A model for DC to DC conversion.

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FIG. 1. An electrical network for which energy is conserved

In order to have a sensible physical model we demand that there be always exactly one path through the inductor

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CONTROLLABILITY ON GROUP MANIFOLDS

LIE ALGEBRAS AND LIE GROUPS

LIE ALGEBRAS AND LIE GROUPS

THEOREM 1 (J. WEI AND E. NORMAN)

THEOREM 2