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On using orthogonal functions with singular systems. (English) Zbl 0552.93033

Singular systems of the form (1) \(E\dot x=Ax+Bu\), \(x(0)=x_ 0\), where \(x\in R^ n\) and \(u\in R^ m\), and E, A and B are constant matrices, appear in many circuit and control applications [see the author, ”Singular systems of differential equations I and II”, London (1980; Zbl 0419.34007) and (1982; Zbl 0482.34008)]. Recently, (1) has been studied using orthogonal functions [see P. N. Paraskevopoulos, IEE Proc., Part D 131, 37-38 (1984; Zbl 0526.93025)]. The interesting approach in the last mentioned paper has a couple of misleading aspects, which this note will attempt to clarify.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
34A99 General theory for ordinary differential equations
93C05 Linear systems in control theory
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