tailieunhanh - Analysis and Control of Linear Systems - Chapter 3

Chapter 3 Discrete-Time Systems Thông thường, một tín hiệu là một chức năng (hoặc phân phối) với sự hỗ trợ trong T không gian thời gian, và có giá trị trong không gian vector E, được định nghĩa trên R. Tùy thuộc vào việc chúng ta có một tín hiệu liên tục thời gian hoặc thời gian rời rạc tín hiệu, không gian thời gian có thể được xác định với tập hợp các số thực R hoặc với các thiết lập của các số nguyên của Z. Một hệ thống rời rạc là một hệ thống, mà biến đổi một tín. | Chapter 3 Discrete-Time Systems . Introduction Generally a signal is a function or distribution with support in the time space T and with value in the vector space E which is defined on R. Depending on whether we have a continuous-time signal or a discrete-time signal the time space can be identified with the set of real numbers R or with the set of integers of Z. A discrete system is a system which transforms a discrete signal noted by u into a discrete signal noted by y. The class of systems studied in this chapter is the class of time-invariant and linear discrete DLTI systems. Such systems can be described by the recurrent equations or 1 x k 1 Ax k Bu k y k Cx k Du k y k any k - n b0u k bnu k - n where signals u x and y are sequences with support in Z kE Z and with value in Rm Rn and Rp respectively. They represent the input the state and the output of the system see the notations used in Chapters 2 and 3 . A B C D ữị bị are appropriate size matrices with coefficients in R Chapter written by Philippe CHEVREL. 1 We can show the equivalence of these two types of representations see Chapter 2 . 82 Analysis and Control of Linear Systems A e Rnxn Be Rnxm C e Rpxn D e Rpxm a e Rpxp b e Rpxm If equations and can represent intrinsically discrete systems such as a .-processor or certain economic systems they are most often the result of discretization of continuous processes. In fact let us consider the block diagram of an automated process through a computer control see Figure . Seen from the computer the process to control which is supplied with its upstream digital-analog and downstream analog-digital converters ADC is a discrete system that converts the discrete signal u into a discrete signal y. This explains the importance of the discrete system theory and its development which is parallel to the development of digital .-computers. Figure . Computer control This chapter consists of three distinct parts. The analysis and .