Answer Happy

(a) [4 marks] Define bounded input bounded output (BIBO) stability and internal stability. (b) [2 marks] Give an example of a linear time invariant (LTI) system that is internally stable but not BIBO stable. (c) [2 marks] Give an example of a LTI system that is BIBO stable but not internally stable. (d) [4 marks] Let x and u be the state and input respectively of a LTI system as in (c); that is, a system that is BIBO stable but not internally stable. (i) Could such a system be internally stabilised by state feedback control, i.e, of the form u = -Kx, where K is a constant gain matrix? Explain and justify your answer. (ii) Could such a system be internally stabilised by state feedback from state estimates produced by a state observer? Explain and justify your answer.