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Design of Analog CMOS built-in Circuits by means of Behzad Razavi
McGraw-Hill Science/Engineering/Math; 1 version (August 15, 2000)
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3 Let X and Y be normed linear spaces and D be an open subset of X . 61) In this case, L(x0 ) := L(x0 )(·) is called the first Fr´echet derivative of Q at x0 , which is denoted by L(x0 ) = Q (x0 ), and dQ(x0 , h) := L(x0 )(h) is called the Fr´echet differential (or simply, F-differentiable) of Q at x0 . Moreover, if Q : D → Y is differentiable at every point x ∈ D, then L(·) = Q (·) is a mapping from D to L(X, Y ), the family of bounded linear operators defined on X with values in Y , and is called the derivative mapping of Q.
13 Nonlinear plant cannot keep the passivity. 14 Obtained passive system by robust controllers. After factorizing the nonlinear plant with unknown perturbations, a robust control scheme is shown to guarantee not only the robust stability of the nonlinear system but also the asymptotic tracking property. Meanwhile, the connection between passivity and robust right coprime factorization is also shown in the obtained equivalent system. 7 is satisfied, the system is robust stable. 2 presents a detailed explanation of the lemma and gives a tracking control design scheme.
Next, we consider a tracking controller based on the exponential iteration theorem. 1. 2. 7. Here, u 1 ∈ U is the reference input, W1 is the space change operator to transform the reference input signal u 1 ∈ U into the real reference input signal r ∈ Y , and C is the designed tracking controller. First, we design a space change operator W1 for the real reference input signal r in space Y so that one of the conditions of the exponential iteration theorem is satisfied. That is, the spaces of r and y are the same.