Generalized Riccati theory and robust control: a Popov by Vlad Ionescu

By Vlad Ionescu

This entire textual content is exclusive in offering a generalization of the algebraic Riccati conception for the indefinite signal and singular circumstances from the viewpoint of the Popov functionality method. the speculation embodies a scientific presentation from the time area, frequency area and state-space standpoints. the total improvement is orientated in the direction of purposes in powerful platforms theory.

  • Extension of the distinguished Popov positivity idea to the sport theoretic case
  • Characterizations of the recommendations to the Riccati equation by way of the input-output operator, move functionality matrix and transmission matrix pencil, all linked to the underlying Hamiltonian system
  • Comprehensive therapy of either non-stop and discrete time cases
  • A signature situation dependent technique which unifies the options to varied mathematical difficulties from powerful keep watch over conception, together with the maxmin, Nehari, H2, H??? regulate and strong stabilization problems
Graduate scholars up to speed engineering and people engaged on the maths of platforms and keep an eye on thought will locate this e-book crucial examining. For researchers, this is often an necessary paintings, whilst looking ever extra strong keep watch over legislation which take uncertainties into consideration.

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Daß im Falln22 kein Regularitätsverhalten in den Spitzen zu fordern ist, wurde von M. Koecher entdeckt. 15 (s. 15 weiter unten) wurden erstmals von M. Eichler mit einer etwas anderen Methode bewiesen [20]. Er benutzte die Fourier-JacobiEntwicklung einer Modulform (s. A IV). § 4. Poincare-Reihen Nach den Thetareihen lernen wir nun ein zweites wichtiges Konstruktionsverfahren für Modulformen kennen. Poincarereihen erhält man durch Mittelung von Funktionen f: ll-I n .....

E, Z* =M

6 Hilfssatz. Wenn das letzte Diagonalelement tnn einer semipositiven Matrix T verschwindet, so T= gilt (~l ~), Tl = Ti n - l )~O. Beweis. Man nutze aus, daß jede zweireihige Unterdeterminante von T nicht negativ ist. 7 Bemerkung. Der

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