By William G. Andrew, H.B. Williams

ISBN-10: 0872010473

ISBN-13: 9780872010475

This quantity covers device engineering details, together with time-saving charts, tables, graphs, and calculations for designers, engineers, and operators.

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Additional resources for Applied Instrumentation in the Process Industries, Volume 3: Engineering Data and Resource Manual

Sample text

We have the following result (Zadeh and Desoer, 1963). 8. ;, i = 1, 2, . . ,I;. Let the i~lttlfiplicit)~ in the characteristic pol~monlialof A be given b)j nl;. Dejne . Ar, is nl,, i = 1 , 2 , . , k; (b) Tlre ii

Let the corresponding clraracferistic uectors be el, e2, . . , en. D e f m the n x n ntafrices . T = (el, e,, . , e,,), A = diag (A,, A,, . . , AJ. 1-77a 1-77b 16 Elemen$ of Linenr System Theory Tlterz T is noruingr~larand A can be represented as A = TAT-'. 1-78 Here the notation 1-77a implies that the vectors e,, e,, . . , e,, are the columns of the matrix T , and 1-77b means that A is a diagonal matrix with A,, A,, . ,A, as diagonal elements. I t is said that T diagonalizes A. The following fact is easily verified.

The time-invariant sj~stein ~ ( t= ) Ax(t) is expairentially stable if arid silly if it is asynrptotically stable. 1-139 Since it is really the matrix A that determines whether a time-invariant system is asymptotically stable, it is convenient to use the following terminology. 6. Tlre 11 x n canstairt inatrix A is asj~itiptoticallystable ifaN its characteristic ualrres haue strictly rregatiue realparts. The characteristic values of A are the roots of the characteristic polynomial det (AI - A). 4 Stability 29 Schwarz and Friedland, 1965) the stability of A can be tested directly from the coefficients of the characteristic polynomial without explicitly evaluating the roots.

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Applied Instrumentation in the Process Industries, Volume 3: Engineering Data and Resource Manual by William G. Andrew, H.B. Williams

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