With the advent of powerful computers,the use of mathemmatical models by mathemmaticians,scri-entists,engineers,and researcher has become models are used for analysis,design,and to predict the behavior of complex These common features provide a unifying framework the systematic and uniform treatment of diverse subject matter which may appear unrelated. | A Practical Approach To Signals Systems and Controls Armando A. Rodríguez Associate Professor Arizona State University Department of Electrical Engineering System Science and Engineering Research Center Tempe AZ 85287-7606 http aar aar@ September 1 1998 Contents 1 Introduction Systems And The Use Of Mathematical Models 7 Widespread Applicability And Common Features Of Mathematical Models . 7 A Unifying Framework The Concept Of A Dynamical System . 8 Linear Systems A Good Tool For Approximation. 9 System Types. 9 2 Mathematical Preliminaries 11 Complex Numbers And Complex Arithmetic . 11 Results From Trigonometry. 22 Results From Calculus. 23 3 Mathematical Models For Continuous Time Signals 27 A Model for Tall Thin Pulse-like Signals Dirac Delta Distribution. 27 A Model for Step-like Signals Unit Step Function . 29 Exponential Signals . 30 Complex Exponential Signals Creating Sinusoids and Exponential Sinusoids . 31 4 An Introduction To Laplace Transforms 35 The Unilateral Laplace Transform An Introduction . 35 Elementary Unilateral Laplace Transforms. 36 Applications. 41 1 2 Signals Systems and Controls . Rodriguez 5 SISO Input-Output Models LTI Systems 57 An Introduction To Linear Systems An Illustrative Example. 57 LTI System Concepts . 58 Natural Response Stability Characteristic Equation And Poles . 64 System Transfer Function. 71 Impulse Response. 75 General Solution And Convolution. 76 Linearity. 77 Time Invariance. 78 Causality. 80 Bounded-Input Bounded-Output BIBO Stability. 81 Step Response . 82 Sinusoidal Steady State Analysis And System Zeros . 86 Frequency Response Magnitude Response Phase Response And Fourier Transform 89 6 Introduction To Bode Plots 93 7 An Introduction To State Space Concepts 103 State Of A System And State Introduction to Descriptor Models State Space Models and MIMO LTI .
