Peter Falb, Publications

On differential in function field, O. Zariski and P Falb, American Jounral of Mathematics, 83, 542-556, 1961.

On the behavior of the geometric genus under ground field extension, P. Falb, American Journal of Mathematics, 84, 421-432, 1962.

Time optimal control for plants with numerator dynamics, M. Athans, P. Falb, R. Kalman and E. Lee, Institute of Electrical and Electronics Engineers, Professional Group on Automatic Control Transactions, AC-7-47-50, 1962.

Time optimal control of a spinning space Body, M. Athans, P. Falb, and R. Lacoss, Institute of Electrical and Electronics Engineers Transactions on Applications and Industry, 67, 204-214, 1963.

Time-, fuel-, and energy-topical control of nonlinear norm-invariant systems, M. Athans, P. Falb and R. Lascoss, Institute of Electrical and Electronics Engineers, Professional Group on Automatic Control Transactions, AC-8, 196-202, 1963.

Time optimal control for a class of nonlinear systems, M. Athans, and P. Falb, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-8, 378-379, 1963.

Optimal control of self-adjoint systems, M. Athans, P. Falb, and R. Lacoss, Institute of Electrical and Electronics Engineers Transactions on Application and Industry, 83, 161-166.

A direct constructive proof of the criterion for complete controllability of time-invariant linear system, P. Falb and M. Athans, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-9, 1989, 1963.

Infinite dimensional control problems I:  on the closure of the set of attainable states for linear systems, P. Falb, Journal of Mathematical Analysis and Applications, 9, 19-22, 1963.

A simple local sufficiency condition based on the second variation, P. Falb, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-10, 348-350, 1965

Reachability of subspaces, P. Falb, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-10, 472-473, 1965.

Remarks on the infinite dimensional Riccati equation, P. Falb and D. Kleinman, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-11, 534-537, 1966.

A note on coverings over imperfect ground fields, P. Falb, American Journal of Mathematics, 88, 447-453, 1966.

One-dimensional minimum time rendezvous for a thrust limited rocket, G. Anderson P. Falb and A. Robinson, American Institute of Aeronautics and Astronautics Journal, 5, 1017-1019, 1967.

On cross correlation bounds and the positivity of certain nonlinear operators, P. Falb and G. Zames, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-12, 219-221, 1967.

On the stability of systems with monotone and odd monotone non-linearities, G. Zames and P. Falb, Institute of Electrical and Electronics Engineers Professional Group on Automatics Control Transactions, Ac-12, 221-223, 1967.

Infinite dimensional filtering:  the Kalman-Bucy filter in Hilbert space, P. Falb, Information and Control, 11, 102-137, 1967.

Decoupling in the design and synthesis of multivariable control systems, P. Falb and W. Wolovich, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control, AC-12, 651-659, 1967.  [Also in Proceedings of the 1967 Joint Automatic Control Conference, Philadelphia, PA].

Stability conditions for systems with monotone and slope-restricted nonlinearities, G. Zames and P. Falb, Society for Industrial and Applied Mathematics Journal on Control, 6, 89-108, 1968.   [Also in “Mathematical Theory of Control,” edited by A. Balakrishnan and L. Neustadt, Academic Press, New York, 313-426.]

On differentials in locally convex spaces, P. Falb and M. Jacobs, Journal of Differential Equations, 4, No. 3, 44-459, July 1968.

Multipliers with real poles and zeros: An application of a theorem on stability conditions, G. Zames and P. Falb, Institute of Electrical and Electronics Engineers Professional Group on Automatic Control Transactions, AC-13, 125-126, 1968.

Topics in Mathematical Systems Theory,” R. Kalman, P. Falb and M. Arbib, McGraw Hill Book Company, pp. 358, Vol. 8, 1969.

Conditions for Optimality, P. Falb and E. Polak, in “Systems Theory,” edited by L. Zadeh and E. Polak, McGraw-Hill Book Company, pp. 489-511, Vol. 8, 1969.

Dolezal’s theorem, linear algebra with continuously parametrized elements and time-varying systems, L. Weiss and P. Falb, Journal of Mathematical Systems Theory, Vol. 4, NO. 1, 67-75, 1969.

A generalized transform theory for causal operators, P. Falb and M. I. Freedman, Society for Industrial and Applied Mathematics Journal on Control, Vol, 7, No. 3, 452-471, 1969.

A multipoint method of third order, W. Bosarge and P. Falb, Journal of Optimalization Theory and Application, Vol. 4, 156-167, 1969.

A Hilbert space stability theory over locally compact abelian groups, M. I. Freedman, P. Falb, and G. Zames, Society for Industrial and Applied Mathematics Journal on Control, Vol. 7, No. 3, 479-495, 1969.

Input-Output stability:  A general viewpoint, P. Falb, M. I. Freedman, and G. Zames.  Fourth Congress of the International Federation of Automatic Control, Warsaw, Poland, June 16-21, 1969, Technical Session No. 41, 3-15.

Some Successive Approximation Method in Control and Oscillation Theory, P. Falb and J. de Jong, Vol. 59 in Mathematics in Science and Engineering, Academic Press, New York, p. 240, 1969.

On the structure of multivariable systems, W. A. Wolovich and P. L. Falb, Society for Industrial and Applied Mathematics Journal on Control, Vol. 7, No. 3, 437-451, 1969.

A note on causality and analyticity, M. I. Freedman, P. L. Falb and J. Anton, Society for Industrial and Applied Mathematics Journal on Control, Vol, 7, No. 3, 472-478, 1969.

On a theorem of Bochner, P. Falb, Institut des Hautes Etudes Scientifiques, Volume dedicated to Professor Oscar Zariski, Extrait, Publications Mathematiques, No. 36, 59-67, 1969. 

Ito’s lemma in infinite dimensions, R. F. Curtain and P. L. Falb, Journal of Mathematical Analysis and Applications, Vol. 31, No. 2, 434-447, 1970.

Infinite dimensional multipoint methods and the solution of two point boundary value problems, W. Bosarge and P. Falb, Numerische Mathematik, Vol. 14, 264-286, 1970.

Transform theoretic approach to the ability of a class of nonlinear partial differential equations, P. L. Falb, M. I. Freedman, and J. Anton, Journal of Differential Equations, Vol. 9, No. 1, 25-45, 1971.

Frequency domain criteria for stability of systems modeled by certain partial differential equations, P. Falb, J. Anton and M. I. Freedman, presented at the symposium IUTAM on “Instability of Continuous Systems,” held at Herrenalb, West Germany, September Systems, H. Leipholz Editor, Springer-Verlag, 1971.

Stochastic differential equations in Hilbert space, R. F. Curtain and P. L. Falb, Jorunal of Differential Equations, V. 10, No. 3, 412-430, 1971.

Bochner’s theorem in infinite dimensions, P. L. Falb and Ulrich Haussmann, Pacific Journal of Mathematics, Vol. 43, No. 3, 601-618, 1972.

Stability of difference approximations to differential equations, P. L. Falb and G. Groome, Journal of Differential Equations, Vol. 13, No. 1, 48-57, 1973.

Linear Systems and Invariants,” P. Falb, Lecture Notes, Control Group, Lund University, Sweden, 1974.

Invariants and canonical forms under dynamic compensation, W. Wolovich and P. Falb, SIAM, J. on Control, 14, 1976.

The role of the interactor in decoupling, P. Falb and W. Wolovich, 1977 Joint Automatic Control Conference, San Francisco.

Invariants and canonical forms under feedback, P. L. Falb and W. Wolovich, Brown University CDS Report LCDS 78-2, 1-46, 1978.

Applications of algebraic geometry in system theory, C. Byrnes and P. L. Falb, American Journal of Mathematics, Vol. 101, 337-363, 1979.

Stochastic integration in measurable spaces, S. Belbas and P. L. Falb, Zeitschrift fur Wahrscheinlich-keitstheorie und Verwandte Gebiete (Berlin), to appear.

“Method of Algebraic Geometry in Control Theory:  Part I:  Scalar Linear Systems and Affine Algebraic Geometry,” P. Falb, Birkauser, 1990.

Dollar Down-Market Up, E. N. Dane and P. Falb, Brown Economic Review, 1995. 

The Main Theorem of Algebraic Linear System Theory, submitted to American Journal of Mathematics, to appear in 1996.

Methods of Algebraic Geometry in System Theory: Part II: Multivariable Linear Systems and Projective Algebraic Geometry, P. Falb (Birkhauser, 1999).

Optimal Control:  An Introduction to the Theory and its Applications, M. Athans and P. Falb, McGraw-Hill Book Company, New York, 879 pp, 1966.   Republished by Dover, 2007.

Pole assignment with parameters, V. Eldem, P. Falb and W. Wolovich, in preparation.

Invariants of subsystems under feedback, P. Falb, in preparation.

Flags, Controllability and the Coordinatization of Systems, P. Falb, in preparation.

Updated 2008