By David Elliott

The mathematical idea of keep an eye on grew to become a ?eld of research part a century in the past in makes an attempt to elucidate and set up a few hard sensible difficulties and the tools used to resolve them. it really is recognized for the breadth of the math it makes use of and its cross-disciplinary power. Its literature, that can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the speculation of linear keep watch over platforms, which mathematically are defined via linear di?erential equations pressured by way of additive regulate inputs. That idea ended in well-regarded numerical and symbolic computational applications for keep an eye on research and layout. Nonlinear regulate difficulties also are vital; in those both the - derlying dynamical approach is nonlinear or the controls are utilized in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical paintings on nonlinear regulate difficulties in keeping with di?erential manifold concept, nonlinear research, and several mathematical disciplines. a number of the difficulties that have been solved in linear keep watch over thought, plus others which are new and pretty nonlinear, were addressed; a few ensuing basic de?nitions and theorems are tailored during this booklet to the bilinear case.

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