Triangular Orthogonal Functions for the Analysis of Continuous Time Systems
Triangular Orthogonal Functions for the Analysis of Continuous Time Systems is a source of new knowledge to researchers and academics in the area of mathematics as well as systems and control. This book deals with a new set of triangular orthogonal functions, which evolved from the set of well known block pulse functions (BPF), a major member of the piecewise constant orthogonal function (PCOF) family. Unlike PCOF, providing staircase solutions, this new set of triangular functions provides piecewise linear solutions with less mean integral squared error (MISE).
After introducing the rich background of the PCOF family, which includes Walsh, block pulse and other related functions, fundamentals of the newly proposed set -- such as basic properties, function approximation, integral operational metrics, etc. -- are presented. This set has been used for integration of functions, analysis and synthesis of dynamic systems and solution of integral equations. The study ends with microprocessor based simulation of SISO control systems using sample-and-hold functions and Dirac delta functions.
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actual solution Analysis and synthesis analysis of linear application approximation block pulse functions BPF domain solution coefficients component functions compute constant orthogonal functions Control Theory delta functions Dirac delta functions Direct expansion DOTF dynamic systems equations 2.34 exact solution expansion of y(x Figure fractional calculus Franklin Instt function f given Haar functions identiﬁcation impulse response integral equation integral squared error LHTF set m-term matrix for integration MISE nonoptimal BPF domain obtained operational matrix optimal and nonoptimal orthogonal triangular function output piecewise constant orthogonal piecewise linear pulse function BPF pulse-width modulated representational error RHTF sample-and-hold functions Sarkar SHOTF shown in Fig SISO control systems solution of equation solve square integrable function squared error ISE synthesis of dynamic Syst system identification TF domain TF domain analysis Theory and Appl tion transfer function triangular function domain triangular function sets vector Walsh functions Walsh matrix ZETOS