CHI-TSONG CHEN KAPITEL 2- Systems Kortfattade läsanvisningar Läs hela kapitlet utom 2.9 och 2.10
2.1. Introduktion Detta är en inledning – du kan koncentrera dig på att förs¨å de kursiverade orden
2.2 CT Systems with and without memory A system is called a memoryless system if its output y(t 0 ) depends only on the input u(t) applied at time t=t 0 A system is called a causal system if its current output depends on past and present inputs, but not on future inputs Every physical system is causal
2.3 The concept of state Antag att du studerar en kropp på ett plant underlag. Kroppen påverkas av en kraft u och kroppens tillstånd kan beskrivas av dess förflyttning (y) och hastighet (v) vid en viss tidpunkt The set of y(t) and v(t) is called the state variable
Lumped system If the number of state variables is finite the system is a lumped system
Zero input response If u(t)=0 for t>0 zero-input response = natural response = unforced response If x(t 0 )=0 zero state response = forced response A system is initially relaxed if x(t 0 )=0 - input before t=0 has no effect
2.4 Linearity of memoryless systems A memoryles system is linear if
Linearity of systems with memory The response of such a system depends not only on the input but also on the initial state. Thus the additivity and homogeneity properties should also apply to the initial state
2.5 Time invariance and its implication If the characteristics of a system do not change with time, the system is said to be time invariant.
2.6. Implication of linearity and time invariance – zero state responses Responses of LTI systems can always be decopmposed into zero-input (natural) responses and zero-state (forced) responses
2.10 Discrete Time LTI-systems
2.11 Conclutions Titta på figur 2.24