## Transform and State Variable Methods in Linear Systems |

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### Contents

Some Basic Concepts I | 3 |

Delta Function | 20 |

Response by Convolution | 43 |

Copyright | |

11 other sections not shown

### Common terms and phrases

5-function analysis analytic apply assumed capacitor Chapter characteristic equation circuit coefficients column complex numbers consider contour convolution integral defined delta function derivative determine developed diagonal difference equations differential equation discrete systems domain eigenvalues eigenvectors electrical networks elements evaluate feedback system Fourier series frequency given by equation gives Hence imaginary axis impulse response inductor infinite input invariant system inversion integral Jordan Jordan normal form Jordan's lemma Laplace transform left half linear systems linear time invariant linearly independent loop Lyapunov function McGraw-Hill multiple network shown Note obtain output partial fractions plane plot poles problem reciprocal basis vectors representation represented residue result RLC network s-plane sampling instants shown in Figure simple singularities sinh solve stability Substituting system matrix system shown system transfer function technique theorem theory transfer function transform method transient unit circle variables voltage write Z-transform