H. Oloomi et B. Shafai, CONSTRAINED STABILIZATION PROBLEM AND TRANSIENT MISMATCH PHENOMENON IN SINGULARLY PERTURBED SYSTEMS, International Journal of Control, 67(3), 1997, pp. 435-454
Citations number
31
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control
We initially study the control of linear systems by state feedback and
simultaneously require the feedback gain matrix to satisfy a certain
constraint equation. We provide two fundamentally different methods to
solve the constrained stabilization problem. The first method paramet
rizes the class of stabilizing gain matrices and converts the problem
to an equivalent nonlinear programming problem. The second method, on
the other hand, converts the problem so an equivalent stabilization pr
oblem by a static output controller where the static gain is required
to take a special structure. The motivation behind introducing this pr
oblem and its solution is the application of the results to the design
of observer based controllers for the singularly perturbed systems. I
t is shown that the transient mismatch phenomenon, which occurs in thi
s type of design, may be alleviated if the observer gain of the fast o
bserver is chosen based on the solution of a certain constraint stabil
ization problem which involves the output matrix of the slow subsystem
.