MAE509 (LMIs in Control): Lecture 11, part B - H2 optimal Full State Feedback and Connection to LQR

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We propose an LMI for H2-optimal full-state feedback. We also show that H2 full state feedback with B1=I minimizes the effect of initial condition on the output. This shows that LQR is a special case of H2 full-state feedback.

Cybernetic Systems and Controls

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I've never seen a system diagram drawn with the inputs coming in from the right and the outputs on the left. Usually it's left to right. Is there a reason for that? I know it's not important, just curious.

BillTubbs

Thank you very much Sir for your course. Please i have a question. Let us consider the following case with an exogenous input w. I have the gain obtained by the H2 optimal control. Now I want to obtain the same gain with the LQR using the H2 formulation. My question is how to choose effectively the good matrices Q and R in order to obtain the same gain as the H2? I saw in slide 16, C1=[Q^(1/2) 0]' and D12=[0 R^(1/2)]'. Does it mean that if C1 and D12 don't have this shape we will never obtain the same gain as the H2 ? That is what i think by considering the mathematical development.

paulchristiantessowoafo

Slide 17 : B1^T*X0*B1 or trace(B1^T *X0*B1) ?

HibaHOUMSI

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