## Orthogonal Functions in Systems and ControlThis book provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi, Gegenbauer, and via orthogonal functions such as sine-cosine, block-pulse, and Walsh. This is the first book devoted to the application of orthogonal polynomials in systems and control, establishing the superiority of orthogonal polynomials to other orthogonal functions. |

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### Contents

Least Squares Approximation of Signals | 36 |

Signal Processing in Continuous Time Domain | 87 |

Analysis of TimeDelay Systems | 127 |

Identification of Lumped Parameter Systems | 157 |

Identification of Distributed Parameter Systems | 183 |

Identification of Linear TimeVarying and Nonlinear | 203 |

Optimal Control of Linear Systems | 213 |

List of Figures | 235 |

Bibliography | 241 |

Author Index | 268 |

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### Common terms and phrases

analysis of linear applied approximation basis functions basis vector block-pulse functions boundary conditions classes of orthogonal coefficients computed control of linear delay operational matrix delay systems derivative operational matrix differential equation differential recurrence relation discrete distributed parameter systems estimate the parameters Example finite Fourier Gegenbauer polynomials Haar functions Hermite polynomials I. R. Horng infinite range orthogonal initial and boundary input integral equations integration operational matrix interval J. H. Chou Jacobi polynomials Laguerre polynomials linear systems linear time-invariant M. L. Wang method obtained optimal control orthogonal functions orthogonal polynomials orthogonal system OSOMRI parameter estimation parameter identification polynomials and sine-cosine pulse functions R. Y. Chang residual error response x(t second kind shifted Legendre polynomials sine-cosine functions solution spectra system described system identification system of orthogonal Systems Science Table Taylor series three-term recurrence formula time-delay systems time-varying systems ur(t Walsh functions Walsh series