By David Elliott

The mathematical idea of regulate grew to become a ?eld of research part a century in the past in makes an attempt to elucidate and manage a few hard sensible difficulties and the equipment used to resolve them. it truly is recognized for the breadth of the math it makes use of and its cross-disciplinary energy. Its literature, that may befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the speculation of linear keep watch over platforms, which mathematically are defined by way of linear di?erential equations compelled by way of additive keep an eye on inputs. That thought resulted in well-regarded numerical and symbolic computational applications for keep watch over research and layout. Nonlinear keep watch over difficulties also are very important; in those both the - derlying dynamical procedure is nonlinear or the controls are utilized in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical paintings on nonlinear keep watch over difficulties according to di?erential manifold conception, nonlinear research, and a number of other mathematical disciplines. the various difficulties that were solved in linear keep watch over thought, plus others which are new and fantastically nonlinear, were addressed; a few ensuing normal de?nitions and theorems are tailored during this publication to the bilinear case.

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