Linear systems.

Exercises for lecture 4 and 5 1. Determine the impulse response of the continuous-time system .ir; = A: + Bu, 3; = 01' + Do with A=[j 3],B=[[11],c=[1 11,1):[1]. . For the system I\": + 1] = 111(k) with 2(0) = [1 0 2]T and b:- II E ab: HMO determine the value of :e(100) applying CayleyHamilton theorem. . For a continuous-time system described by t) = A320?) 1with -1 1 or A = 0 2 1 0 1 0 determine all the values of or E 32 such that the system contains as few modes as possible. . Analyze asymptotic and Lyapunov stability of the origin I = U of the system described by - 2 $1 = 1.'11.'2, 3.2 = 3$$2. . Consider a. system given by x\": + 1) = Ax(k} with e. b A=|:_b a]. Determine some values of mi: E 33, (1,!) ;IE 0 such that the origin is stable but not asymptotically stable