System Analysis via Orthogonal Functions

  • Alexander Weinmann


Classical orthogonal polynomials, generalized and shifted orthogonal polynomials serve as an excellent tool for modelling plants and processes in an approximative way. Moreover, solutions via orthogonal polynomials give a straightforward algorithm in reducing various dynamic problems to the solution of a set of algebraic linear equations. The integral of a function with respect to time is replaced by premultiplying the vector of the decomposed signal by an operational matrix. Furthermore, the product of functions and even timevarying coefficients and nonlinear relations are reduced to algebraic manipulations. Among these problems are system analysis, variational calculus, optimal control, identification and model reduction. Orthogonal functions have been applied in control measurement and correlation techniques for a long period, see e.g. Kitamori, T., 1960; Douce, J.L., and Roberts, P.D., 1964. The classical Fourier series expansion, truncated to a certain amount of terms, can also be applied to solve various dynamic problems (Paraskevopoulos, P.N., et al. 1985; Cheok, K.C., et al. 1989).


Orthogonal Polynomial Operational Matrix Functional Differential Equation Power Series Expansion State Feedback Controller 


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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Alexander Weinmann
    • 1
  1. 1.Department of Electrical EngineeringTechnical University ViennaAustria

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