Spaces of Observables in Nonlinear Control

Eduardo D. Sontag
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Eduardo D. Sontag: Rutgers University, Department of Mathematics

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1532-1545 from Springer

Abstract: Abstract Engineering design and optimization techniques for control typically rely upon the theory of irreducible finite–dimensional representations of linear shift–invariant in–tegral operators. A representation of $$ F:{[{L_\infty }{,_{loc}}(0,\infty )]^m} \to {[{C_0}(0,\infty )]^p}$$ is specified by a triple of linear maps $$ A:{\mathbb{R}^n} \to {\mathbb{R}^n},B:{\mathbb{R}^m} \to {\mathbb{R}^n},{\text{ }}and{\text{ }}C:{\mathbb{R}^n} \to {\mathbb{R}^p}$$ so that, for each “input” $$ \omega ,F(\omega )(t) = C\xi (t),$$ where the state ξ is the solution of the initial value problem $$ \xi '(t) - A\xi (t) = B\omega (t),\xi (0) = 0.$$

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_150

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