Time varying linear discrete-time systems. II. Duality

Bostwick Frampton Wyman

Vol. 86 (1980), No. 1, 361–377

DOI: 10.2140/pjm.1980.86.361

Abstract

This paper treats questions of duality for time-varying linear systems defined on a locally finite partially ordered time set. Difference equations are studied by considering the state space of the system as a module over the incidence algebra of the poset, and dual systems can be described abstractly. The resulting dual system gives the evolution equations (in reverse time) for the Lagrange multipliers associated to standard linear-quadratic optimal control problems.

Mathematical Subject Classification 2000

Primary: 93C05

Secondary: 93C50

Milestones

Received: 12 April 1978

Revised: 5 September 1978

Published: 1 January 1980