13_Sys_Properties

13_Sys_Properties - Chapter 13 Properties of Systems...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
437 Chapter 13 Properties of Systems Chapter Outline 13.1 DEFINITION OF THE SYSTEM PROPERTIES. .................................. 439 13.1.1 Introduction. ............................................................................................................................... 439 13.1.2 System Properties. .................................................................................................................. 439 13.1.3 Derivation of the Convolution Integral. ........................................................................ 443 13.1.4 Summary. .................................................................................................................................... 445 13.2 DISCUSSION OF PROPERTIES OF SYSTEMS. 446 13.2.1 Introduction. 446 13.2.2 Causality. 446 13.2.3 Linearity and Time Invariance. ........................................................................................ 446 13.2.4 Relaxed . ...................................................................................................................................... 449 13.2.5 A Mechanical System. ......................................................................................................... 449 13.3 BIBO STABILITY. .............................................................................. 452 13.3.1 Introduction. 452 13.3.2 Definition of BIBO Stability . ............................................................................................ 453 13.3.3 Convolution Integral. ............................................................................................................. 455 13.4 BIBO STABILITY OF TRANSFER FUNCTIONS AND STATE SPACE REPRESENTATIONS. 457 13.4.1 Introduction. 457 13.4.2 BIBO Stability of Transfer Function Representations . ......................................... 458 13.4.3 BIBO Stability of State Space Representations. ..................................................... 463 13.5 PROPERTIES OF SYSTEM REPRESENTATIONS. ............................. 465 13.5.1 Introduction. 465 13.5.2 The Convolution Integral. ................................................................................................... 465 13.5.3 Transfer Functions. ................................................................................................................. 467 13.5.4 State Space Equations. ........................................................................................................ 468 13.5.5 Fourier Transfer Function . .................................................................................................. 468 13.5.6 Summary. 469 13.6 STATIC NONLINEARITIES. ............................................................... 469 13.6.1 A Nonlinear System . 469 13.6.2 Graphical Construction of the Output Signal from a Nonlinearity. ................. 471 13.6.3 Summary. 472 13.7 CHAPTER SUMMARY. ....................................................................... 473 13.8 HOMEWORK FOR CHAPTER 13. ...................................................... 475 In this chapter we take a more abstract view of a system. Starting with the basic definition of a system, we introduce four properties of this system. These four
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
438 Chapter 13 Properties of Systems properties are: causality, linearity, time invariance, and relaxed. It is then shown that these four properties can be used to derive the convolution representation. We have already established that the convolution representation is closely related to the Laplace transfer function, the Fourier transfer function, and state space representations. So from a mathematical viewpoint, these four properties essentially define all of these system representations. This abstract characterization of system representations has several practical implications. In order for system analysis to be useful, the system representation must match the observed physical process. The system properties introduced above are a basic link between the experimentally observed data and the system representation used to model the process. Often we can directly verify if the physical process satisfies (or doesn’t satisfy) the four properties above. Hence, these properties can be used to determine if the system representations are appropriate models for the observed physical process. The four system representations we are focusing on in this text are in many ways essentially equivalent. There are some differences between them, however. The four system properties we will introduce in this chapter will allow us to distinguish between these system representations. By carefully characterizing each system representation, we gain insight into selecting the proper system representation to model a certain system. It is the purpose of this chapter to explore the similarities and differences between these system representations.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/10/2009 for the course ECE 60367 taught by Professor Meehan during the Spring '09 term at Virginia Tech.

Page1 / 48

13_Sys_Properties - Chapter 13 Properties of Systems...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online