Explicit MPC of LPV systems in the controllable canonical form

Constrained Control and Estimation of Homogeneous Reaction Systems Using Extent-Based Linear Parameter Varying Models

“…This is the case when a perfect mass controller is implemented and the outlet f low is given by u out (t) = u i p in i 1 , ∑ = . Based on the work of Kvasnica et al, 27 and the polytopic nature of Θ, the following lemma can be stated: Lemma 1. Let i  be a set defined as…”

“…The proof of the lemma can be seen in ref 27. Now, by stacking vectors with future states and control inputs, eq 21 can be written as…”

“…Based on the work of Kvasnica et al, and the polytopic nature of Θ, the following lemma can be stated:…”

“…The proof of the lemma can be seen in ref . Now, by stacking vectors with future states and control inputs, eq can be written as where , , K̃ d = [ K d T , ..., K d T ] T , and K̃ (σ i ) = diag­([ K (σ i ), ..., K (σ i )]).…”