Continuous-Time Systems

Abstract

1 Introduction. 1.1 Principles of Operation of Typical Systems. 1.2 Systems Performance and Classification. 1.3 Basic Structures. 1.4 Basic Operations with Signals in Systems. 1.5 Summary. 1.6 Problems. 2 Quantitative Methods of Systems Description. 2.1 System Responses to Test Signals. 2.2 Methods for Linear Systems. 2.3 Common Methods for Nonlinear Systems. 2.4 Approximation and Linearization. 2.5 Averaging. 2.6 Equivalent Linearization. 2.7 Norms. 2.8 System Stability. 2.9 Summary. 2.10 Problems. 3 Qualitative Methods of Systems Description. 3.1 Qualitative Analysis. 3.2 Phase Trajectories. 3.3 Bifurcations. 3.4 Chaotic Orbits and Fractals. 3.5 Conservative Systems. 3.6 Dissipative (Near Conservative) Systems. 3.7 Summary. 3.8 Problems. 4 LTI Systems in the Time Domain. 4.1 Introduction. 4.2 Convolution. 4.3 Presentation by Differential Equations. 4.4 Electric Circuit Presentation by ODEs. 4.5 System Simulation by Block Diagrams. 4.6 State-space Presentation. 4.7 Solution of State Space Equations. 4.8 Summary. 4.9 Problems. 5 LTI Systems in the Frequency Domain (Transform Analysis). 5.1 Introduction. 5.2 Fourier Analysis. 5.3 Laplace Transform. 5.4 Unilateral Laplace transform. 5.5 Applications of Laplace transform. 5.6 Stability Analysis of Feedback Systems. 5.7 Selective Filter Approximations. 5.8 Summary. 5.9 Problems 6 Linear Time-Varying Systems. 6.1 Introduction. 6.2 Time-varying Impulse Response and General Convolution. 6.3 Properties of LTV Systems. 6.4 Differential Equation Presentation. 6.5 State Space Presentation. 6.6 Linear Periodically Time-varying Systems. 6.7 Summary. 6.8 Problems. 7 Nonlinear Time Invariant Systems. 7.1 Introduction. 7.2 Memoryless Systems. 7.3 Presentation of Memory Systems by Volterra Series. 7.4 Representation in the Transform Domain. 7.5 Approximation by Describing Functions. 7.6 Description by Differential Equations. 7.7 State Space Presentation. 7.8 Summary. 7.9 Problems. 8 Nonlinear Time Varying Systems. 8.1 Introduction. 8.2 Memoryless Time-varying Nonlinearities. 8.3 Volterra Series Expansion. 8.4 Description by Differential Equations. 8.5 Nonlinear Periodically Time-varying Systems. 8.6 State-space Presentation. 8.7 Summary. 8.8 Problems. A Dirac Delta Function. B Matrices. C Tables of Fourier Series, Transform, and Properties. D Tables of Laplace Transform and Transform Properties. E Mathematical formulas. References. Index.