By Jean-Michel Coron
This publication offers ways to examine the controllability and the stabilization of nonlinear keep watch over platforms in finite and countless dimensions. The emphasis is wear particular phenomena because of nonlinearities. specifically, many examples are given the place nonlinearities change into necessary to get controllability or stabilization. a number of equipment are offered to review the controllability or to build stabilizing suggestions legislation. the ability of those tools is illustrated by means of a variety of examples coming from such parts as celestial mechanics, fluid mechanics, and quantum mechanics. The booklet is addressed to graduate scholars in arithmetic or keep watch over idea, and to mathematicians or engineers with an curiosity in nonlinear keep an eye on structures ruled via traditional or partial differential equations.
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Extra info for Control and Nonlinearity (Mathematical Surveys and Monographs)
Example text
1 Límite de una función MJTE DE U N A FU 75 N ( 1111�ideremos la funcíón f definida por la ecuación /(X) 2 2x + X x-1 t::: - 3 (1) 1 lhscrvemos quef(x) . cuando x 1,¡ l uncton se aproxime a 1 , pero no llega a ser igual a existe para toda x excepto x = 1 . Se investigará n los valores de 1 . El siguie nte ejemplo . tlmt rattvo muestra la forma en que podría obtenerse la funci ón definida por (1) y la 1 1116n por la cual se deben considerar dichos valor es de la función. • EJEMPLO 1 LUSTRATIVO 1 111 l'Cuación Y = 2x + x - 1 · ....
11 33. r) (a� �ot 1 está definida y (b) sec t no está def1111da. � 34. ) En los ejercidos 35 a 38, determine tan O cuantl� es el ángulo entre las rectas que tienen las pendlr tes dadas. }; (b) 4 Y -� 36. (a) t y -i; (b) t Y ! 37. (a) -t y �; (b) -1 Y -� 38. (a) - � y 2; (b) -t Y -+o 35. (a) 1 y lu� r�•ctas que tienen las ecuaciones 2x + tl O, 3x -y - 4 = O, y 3x + 4y + 8 = lunn redondeando a grados, las medidas lm 1\u¡¡ulos interiores del triángulo que tiene th 1� en ( 1 , 0), (-3, 2) y (2, 3).
Véase l a Figura 7 . fiGURA 8 Figu ra 8, o ... 51 y En la parte (d), nótese que, aun cuando x - 1 está definida para todos Jos valores de x, el dominio de g j, de acuerdo con la definición de función compuesta, es el con junto de todos los números x en el dominio dejpara los quej(x) está en el dominio de g. f. • Funciones ; (a) La función definida porj(x) = 5 es constante, tld eje x. (b) La función definida por g(x) = -4 es constante y su gráfica es una línea hori/Ontal 4 unidades por debajo del eje x.