T. Iwasaki et Re. Skelton, ALL CONTROLLERS FOR THE GENERAL H-INFINITY CONTROL PROBLEM - LMI EXISTENCE CONDITIONS AND STATE-SPACE FORMULAS, Automatica, 30(8), 1994, pp. 1307-1317
Citations number
28
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control
This paper presents all controllers for the general H(infinity) contro
l problem (with no assumptions on the plant matrices). Necessary and s
ufficient conditions for the existence of an H(infinity) controller of
any order are given in terms of three Linear Matrix Inequalities (LMI
s). Our existence conditions are equivalent to Scherer's results, but
with a more elementary derivation. Furthermore, we provide the set of
all H(infinity) controllers explicity parametrized in the state space
using the positive definite solutions to the LMIs. Even under standard
assumptions (full rank, etc.), our controller parametrization has an
advantage over the Q-parametrization. The freedom Q (a real-rational s
table transfer matrix with the H(infinity) norm bounded above by a spe
cified number) is replaced by a constant matrix L of fixed dimension w
ith a norm bound, and the solutions (X, Y) to the LMIs. The inequality
formulation converts the existence conditions to a convex feasibility
problem, and also the free matrix L and the pair (X, Y) define a fini
te dimensional design space, as opposed to the infinite dimensional sp
ace associated with the Q-parametrization.