A method is proposed for approximating the reachable set from the origin for a class of n first order linear ordinary differential equations subject to bounded control. The technique involves decoupling the system equations into 1- and 2-dimensional linear subsystems, and then finding the reachable set of each of the subsystems. Having obtained bounds on each of the decoupled state variables, a n-dimensional parallelpiped is constructed which contains the reachable set from the origin for the original system. Several illustrative examples are presented for the case where the control is a scalar. The technique is also compared to a Lyapunov approach of approximating the reachable set in a simple 2-dimensional example.

"The purpose of this paper is to present some of the elementary results of abstract set theory. This will include the definition of an 'order' relation for cardinal numbers, and a discussion of whether or not this definition defines a simple ordering of the cardinals. Although we will not answer this question fully, in the course of the discussion a key theorem (the Bernstein Theorem) will arise. The remainder of the paper will be devoted to a discussion of this theorem, its proof, a generalization due to Banach, a discussion of this proof, and a generalization of Banach's Theorem by Ky Fan"--Introduction. / Typescript. / "February, 1958." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaf 25).

Thesis (M.S.)--Oregon State University, 1972. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

No description available.

No description available.

Thesis (M.Sc.) -- University of Adelaide, Dept. of Pure Mathematics, 1972.

Thèse--Université de Paris. / Bibliography: p. [159-162].

Thesis (doctoral)--Universität Bern, 1913. / Includes bibliographical references (p. [137]-138).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thèse--Université de Paris. / Bibliography: p. [159]-[162].