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Elliott1 1University of Maryland Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved. pub2 Article Online Posting Date: July 13, 2007 Abstract | Full Text: HTML PDF (233K) ● ● ● ● Recommend to Your Librarian Save title to My Profile Email this page Print this page Browse this title ● Search this title Enter words or phrases ❍ ❍ ❍ Advanced Product Search Search All Content Acronym Finder Abstract This article contains necessary background on linear control systems; the definition of bilinear systems and some sources of BLS in engineering; a guide to some useful system theoretic methods; the application of these methods to problems such as stabilization, observability, and controllability; and brief accounts of areas where BLS have made a major contribution to system theory.

Linear systems, there is a simple and useful condition necessary for controllability. Stated for equation 1, this Kalman rank condition is k x˙ = Ax + k x˙ = If it is satisfied, the matrix-vector pair {F, g} is called a controllable pair. If the controls are not bounded, this condition is sufficient for controllability, but if they are in some Uµ , the control may be small compared with Fx for large x and have an insufficient effect. BILINEAR SYSTEMS: WHAT, WHY, WHERE? Precisely what are BLS and why should one use bilinear systems in control engineering?

This section will give some answers to those questions, starting with a formal definition, and give some examples. Definition. A bilinear system is a first-order vector differential equation x˙ = p(x, u) in which x is a state vector; u is a control signal (scalar or vector); and the components of p(x, u) are polynomials in (x, u) that are linear in x, u separately, but jointly quadratic, with constant real coefficients. Restating that, for any real numbers α, β p(αx, βu) ≡ αβ p(x, u) + α p(x, 0) + β p(0, u) The (optional) output is linear, y = h x.

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04.Automatic Control by John G. Webster (Editor)


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