The name is absent



18

where the time constants are

T^L = Cτn∕∂Li ^^Na — Cm∣ C)Na, and 7⅛ — Cm∕ Qκ∙

Representing the quasi-active system as a linear system permits both an analytic solu-
tion via the eigenvalue decomposition and also a description of the resonant behavior
of (2.3) in terms of the eigenvalues of A.

Recall that the linear system given in (2.12) has the analytic solution

z{t) = eAt ( [ e~AsBu(s)ds + z(0)^ .                 (2∙14)

Vo              /

Assuming A is diagonalizable, it has an eigenvalue decomposition

A = RAIZ-1,                           (2.15)

where A is a diagonal matrix. That is, the jth column of V is the eigenvector corre-

Sponding to the eigenvalue A7 =

z(t) = VeAt

n

=Σ'∙

J=I

= Λj∙j∙. Then substituting (2.15) into (2.14) yields

( /" e~Ascu(s)ds + z(0)^

Vo              /

r∙je^t f [ e~λjsCju(s)ds + ¾(0)λj ,
’ ∖Jo                        /

where c = V λB, which is a vector in this example system. The integral can be





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