2. Consider the system described by1 00 -10 -11i(t)x(t) +0 u(t)1-11y(t) = [ 0 0 1]r(t)0 0 1]r(1)a) Find the modes of the system.b) For each mode, determine whether or not that mode is (i) controllable; (ii) observable.Explain your answers.c) Determine whether or not the system is (i) stabilizable; (ii) detectable. Explain your answers.d) Determine whether or not the system is (i) stable in the sense of Lyapunov; (ii) asymptoticallystable; (iii) globally asymptotically stable; (iv) bounded-input bounded-output stable; (v)critically stable. Explain your answers.e) Is it possible to asymptotically stabilize this system by using(i) Static output feedback of the form u(t) = Ky(t), where K is a constant gain.(ii) Dynamic output feedback of the form û(s) = C(s)ŷ(s), where C(s) is a proper andrational transfer function.(iii) State feedback of the form u(t) = K«(t), where K is a constant matrix.(iv) Repeat part (i) for the case when the output equation is changed to:v(t) = [ 1 0 0]¤(t)In each case, if your answer is positive, design such a controller; if your answer is negative,explain the reason.

Note: As per bartleby instruction when more then three questions for subpart is given only three…

1 1 0 -1 0 -1 æ(t) + 0 u(t) ¿(t) : 1 = -1 1 v(t) = [ 0 0 1]=(t) a) Find the modes of the system. b) For each mode, determine whether or not that mode is (i) controllable; (ii) observable. Explain your answers. c) Determine whether or not the system is (i) stabilizable; (ii) detectable. Explain your answers.

1 1 0 -1 0 -1 æ(t) + 0 u(t) ¿(t) : 1 = -1 1 v(t) = [ 0 0 1]=(t) a) Find the modes of the system. b) For each mode, determine whether or not that mode is (i) controllable; (ii) observable. Explain your answers. c) Determine whether or not the system is (i) stabilizable; (ii) detectable. Explain your answers.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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