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3.1 The norm used in the definitions of stability need not be the usual Euclidian norm. If the state- space is of finite dimension n (i.e., the state vector has n components), stability and its type are independent of the choice of norm (all norms are "equivalent"), although a particular choice of norm may make analysis easier. For n = 2 , draw the unit balls corresponding to the following norms: (i) || x || = (x1)² + (x2)? (Euclidian norm) %3D (ii) || x ||? = (x, )² + 5 (x2)? (iii) || x || = |x|| + |x2]

3.1 The norm used in the definitions of stability need not be the usual Euclidian norm. If the state- space is of finite dimension n (i.e., the state vector has n components), stability and its type are independent of the choice of norm (all norms are "equivalent"), although a particular choice of norm may make analysis easier. For n = 2 , draw the unit balls corresponding to the following norms: (i) || x || = (x1)² + (x2)? (Euclidian norm) %3D (ii) || x ||? = (x, )² + 5 (x2)? (iii) || x || = |x|| + |x2]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.1 The norm used in the definitions of stability need not be the usual Euclidian norm. If the state- space is of finite dimension n (i.e., the state vector has n components), stability and its type are independent of the choice of norm (all norms are "equivalent"), although a particular choice of norm may make analysis easier. Forn=2, draw the unit balls corresponding to the following norms: || x ||? = (x,)² + (x2)? (Euclidian norm) %3D (ii) || x || = (x))² + 5 (x2)? (iii) || x || = |x|| + |x2l
Transcribed Image Text:3.1 The norm used in the definitions of stability need not be the usual Euclidian norm. If the state- space is of finite dimension n (i.e., the state vector has n components), stability and its type are independent of the choice of norm (all norms are "equivalent"), although a particular choice of norm may make analysis easier. Forn=2, draw the unit balls corresponding to the following norms: || x ||? = (x,)² + (x2)? (Euclidian norm) %3D (ii) || x || = (x))² + 5 (x2)? (iii) || x || = |x|| + |x2l
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