In this short lecture, we combine the LFT, the KYP Lemma, Schur complement, Duality, and Variable Substitution to find an LMI for Hinfinity optimal full-state feedback controller synthesis.
Sir the 2nd point in Theorem 5 is an LMI in two variables which are Y and Z. I wanted to know if interpreted that correctly or not? And if that is correct how do we solve for two variables with just one equation?
Mister, thanks a lot for such riveting content. If I may ask a question, how can we know the shape and entries' value of B1 and D11? I do not really get the meaning of D11. Is it free decisionning for the conceptor? Based on its position in the KYP matrix, D11 only constraints the objective variable gamma's value and not Y and Z, is not it? About B1, I suppose that its shape depends on the type of disturbances we are considering. However, what about its entries' value? Thanks a lot.
D11 is the direct feed-through term. It is significant if the disturbance is measured directly in the regulated output, as is the case in the tracking framework, where e(t)=y(t)-r(t) is regulated and r(t) is the reference signal which we treat as a disturbance. The number of rows in B1 is the number of states, and the number of columns is the number of disturbances. The values will depend on the system you are modelling, so its hard to say a priori.
Because we are looking for K here and not u, it doesn't fit directly in the controller synthesis framework. Two typical options: 1) formulate directly as an optimization problem in terms of (Lecture 2), e.g. dynamic programming or MPC. 2) weight your actuation signal heavily in the regulated output and hope for the best.
Hello Dr. Peet, is it possible to derive an LMI where both u and w use static state-feedback (u=Fx, w=Lx), I've seen hamiltonian derivations for the solution. But have not been successful in forming such an LMI, pure curiosity.
Hello dear doctor I have a state space model with 2 equations in this form (X(k+1)=Ax+dw+Bu and Y(k)=Cx+Du), so, please,how can represente the 9 matrices form that?
@@MatthewPeet but please, Dr. Do you have a matlab code for example that design H infinity controller with uncertainty in lmi because I don't deal with robust Control before??
