The paper describes the set of solutions of the discrete-time algebraic Riccati equation. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix of an unmixed solution. The results of the paper provide an extended counterpart of the parametrization theory of...

If two solutions Y ≤ Z of the DARE are given then the set of solutions X with Y ≤ X ≤ Z can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y . The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.

Adams, J. C. (1958). Outline of Fractures, Including 7oint Injuries, 2nd ed., p. 70. Livingstone, Edinburgh. Brickner, Wm., and Milch, H. (1926). International Clinics, 36, 1, 216. Gaston, S. R., Smith, F. M., and Baab, 0. D. (1949). Amer. 7. Surg., 78, 631. Metcalfe, R. F. (1926). Surg. Gynec. Obstet., 34, 270. Patrick, J. (1940). Brit. 7. Surg., 27, 108, 737. Smillie, I. S. (1962). Injuries o...

The relation between Markovianity and representability by means of first-order PDEs is investigated. We consider two versions of the Markovian property, weak and strong-Markovianity. The weak version has been introduced in [J.C. Willems, State and first-order representations, in: V.D. Blondel, A. Megretski (Eds.), Unsolved Problems in Mathematical Systems & Control Theory, Princeton University ...

This document reports on the T28 experiments on multi-modal interaction in bathroom design Author: Louis Vuurpijl, Stéphane Rossignol, Norbert Pfleger, Louis ten Bosch, Ralf Engel, Don Willems, Lou Boves Reviewers: Lou Boves

A new genus and new species of the family Cletopsyllidae Huys & Willems, 1989 from deep-sea sediment in the Gulf of Mexico, are reported and fully described and illustrated. The new genus Pentacletopsyllus (type species: P. montagni sp. n.) can be distinguished from the four known genera of the family by antennule segmentation, length ratio of first and second endopodal segments of P1, and arma...

It is well known that the controllability of a linear multidimensional control system depends on an algebraic property (namely, the torsion-freeness) of a certain module M associated with the system (Oberst, 1990; Pillai and Shankar, 1999; Pommaret and Quadrat, 1999a; 1999b). The recent survey (Wood, 2000) gives different equivalent formulations of controllability and, in particular, the equiva...

BRIEF REPORT Authors Erwin Kemna, Harold Tjalsma, Coby Laarakkers, Elizabeta Nemeth, Hans Willems, Dorine Swinkels Department of Clinical Chemistry, Radboud University Nijmegen Medical Centre, Nijmegen, The Netherlands. Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA, USA. Corresponding author Erwin H.J.M. Kemna Department of Clinical Chemistry...

Group systems are a generalization of Willems-type linear systems that are useful in error control coding. It is shown that the basic ideas of Willems’s treatment of linear systems are easily generalized to linear systems over arbitrary rings and to group systems. The interplay between systems (behaviors) and trellises (evolution laws) is discussed with respect to completeness, minim&y, control...

This paper revisits the definition of linear time-invariant (LTI) stochastic process within a behavioral systems framework. Building on Willems (2013), we derive a canonical representation of an LTI stochastic process and a physically grounded notion of interconnection between independent stochastic processes. We use this framework to analyze the invariance properties enjoyed by distances betwe...