22_Dis_Sys_Prop

22_Dis_Sys_Prop - Chapter 22 Properties of Discrete-Time...

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859 Chapter 22 Properties of Discrete-Time Systems Chapter Outline 22.1 PROPERTIES OF SYSTEMS . ............................................................. 861 22.1.1 Introduction. ............................................................................................................................... 861 22.1.2 Definitions. ................................................................................................................................. 861 22.2 PROPERTIES OF SYSTEM REPRESENTATIONS. ............................. 863 22.2.1 Introduction. 863 22.2.2 Derivation of the Convolution Representation . ........................................................ 864 22.2.3 Properties of Difference Equations. ................................................................................ 865 22.2.4 Properties of Transfer Functions. ..................................................................................... 866 22.2.5 Properties of State Space Representations . ............................................................... 867 22.2.6 Summary. .................................................................................................................................... 868 22.3 BIBO STABILITY. .............................................................................. 868 22.3.1 Definitions. 868 22.3.2 The Convolution Representation. .................................................................................... 869 22.3.3 Transfer Functions. ................................................................................................................. 871 22.3.4 State Space Representations . ........................................................................................... 874 22.4 RELATIONSHIPS BETWEEN SYSTEM REPRESENTATIONS. .......... 875 22.4.1 Introduction. 875 22.4.2 Relationships Between System Representations . ................................................... 876 22.4.3 Summary. 879 22.4.4 MATLAB Experiments. ....................................................................................................... 880 22.5 CONTINUOUS-TO-DISCRETE SYSTEM TRANSFORMATIONS. ........ 881 22.5.1 Introduction. 881 22.5.2 Discretization . .......................................................................................................................... 882 22.5.3 MATLAB Experiments. 884 22.6 CHAPTER SUMMARY. ....................................................................... 885 22.7 HOMEWORK FOR CHAPTER 22. ...................................................... 888 The primary purpose of this chapter is twofold. First, we will introduce several basic properties of systems. These properties serve to characterize a system in terms of easily checked criteria. This classification of systems determines which tools can be used for the analysis of the system, for example. Hence, these properties are of fundamental importance in understanding systems. After we have defined these system properties, we will determine the system properties of each of the system representations we introduced in the last chapter. Once again we find that the theory we develop for discrete-time systems is an exact parallel to the theory developed for continuous-time systems. In fact, the
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860 Chapter 22 Properties of Discrete-Time Systems definitions of properties of systems we introduce in this chapter are exactly the same as the properties defined in Chapter 13. Most of the results in this chapter are parallels to the results in Chapter 13, with the notable exception of the stability results. Comparisons with the continuous-time results are made throughout the chapter. Second, we will develop the interrelationships between the system representations we have introduced in the previous chapter. These interrelationships are used in the routine analysis of systems. System analysis typically proceeds in several stages. At each stage, different tools may be applied to further enhance the understanding of the system. The particular analysis tool depends on the system representation. To switch between analysis tools requires that we switch between system representations. Hence, the interrelationships between the representations play a key role in system analysis. For example, all computer analysis tools, such as MATLAB, have built-in commands to effect these system conversions. The properties of systems developed in the first part of the chapter are used in the development of the interrelationships between the systems.
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22_Dis_Sys_Prop - Chapter 22 Properties of Discrete-Time...

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