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19), it suffices to choose the following approximation for the disturbing-action spectrum: Sϕ (ω) = 2 1 + k2 ω2 . 18) is therefore fulfilled. Thus, the optimal controller design for k = 0 presents a well-posed problem. Using the same synthesis algorithm, we obtain the following mathematical model for the optimal controller: [(3 − 11k)D − (5 + 3k)]u = 12[(1 + 3k)D + 4]x. 26) Then, the characteristic polynomial of the closed system is ∆ = (20k − 3ε + 11εk)D2 + (20 + 12k + 5ε + 3εk)D + 12. 27) Chapter 1.

12). Noncanonic equations and sets of such equations were examined by V. A. Steklov (1927). In several last decades, these equations, although frequently met in applications and having many interesting properties, have been paid undeservedly little attention. Now, it is easy a matter to establish a simple criterion making it possible to discriminate between well- and ill-posed problems in solving systems of linear differential equations with constant coefficients. To do this, it suffices to construct the “degree matrix”, i.

Note that, mathematically, a “controller” is an arbitrary relation between the control action, or the control, u and some controlled variables xi . 26) exemplify such relations; these relations are to be subsequently embodied in technical devices also called “controllers”. A. M. Letov found that, for rather widely encountered linear control objects mathematically modeled with systems of linear differential equations written in the normal form ⎧ ⎪ ⎨ x˙ 1 = a11 x1 + . . 1) ........................

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