16 Stability aird Feedback Systems 400 Exercise 16.1 Ttnc stability of a system with irnpiilse rcsponsc? h(t) = t”-O It sin(5nt),c(f) is to be iriwstigated a) Can the impulse response be absolutely iril egra,tetl’? b) Check tlir location of tlie poles xercise 16.2 Show that (16.7) is a iiecessarg and sufficient condition for the BIBO-stability of a disrrtlte ILTI-sysLern Zxercise 16.3 ten1 is described by the following diffec.rrnitia1equation: - 61 with < \ U \< 00 33 a ) Dcteriniiir If,( ) = and the corresponding polr-wro diagram Give he ROC of I I , ( z ) For what values of a is the b) miiic the trariskr lunction H Z ( z ) of a second d IIz( cc.) = Givc both p c ible KOCs of N J each whether it is st;tblc s system so that cl clet wmine for Exercise 18.4 A system is giver1 by thc differcntial equation yrk] - ;v[k - I] -t- $y[k - 21 = ~ [ k ] a ) Giw t h c transfer function N ( z ) = x(z) of the system b) Tr thc spslcm stable‘? This slionld be tlcttrrriined a ) with tthe pole-zero diagram, a) with the biliizear traiisforiiiation z = and a stability test for continuous loystcms c ) Is the system minimal p h w ? tl) 1s the systcrri causal:“ Exercise 16.5 Uriiig tlic internal coiiipoyicnt of the out piit, sigital giw a mothratioii that r2 discrctc system is stablc if its poles lie within the w i t circle of tlic complex z-plme (see Section 16.2.2)