Solutions to the H∞ general distance problem which minimize an entropy integral
✍ Scribed by D. Mustafa; K. Glover; D.J.N. Limebeer
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 587 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0005-1098
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✦ Synopsis
We pose, and solve, the problem of minimizing the entropy of an H~-norm bounded and stabilized closed-loop. Solution proceeds via the equivalent error system distance problem. The central member of the admissible class is shown to minimize the entropy at infinity, and in that case an explicit state-space formula is derived for the minimum value of the entropy. Links between entropy, H2-norms and H2-optimal control are given.
Notation
The notation
X=Ric[_cml. C -nAB;]
means that X = X T is the stabilizing solution of the algebraic Riccati equation
XA + ATx --XBBTX + cTc = O.
State-space realizations will be written A B s
A square transfer function matrix G(s) is said to be all-pass if a*(j~o)G(jco) = t, V~o.
The Laplace transform variable s will be suppressed for notational simplicity. All transfer function matrices are taken to have real-rational elements; all constant matrices are taken to have real elements. Other notational conventions are listed below.
~H2
~H~
L{G}
The open right half plane.
(Prefix) real-rational. Hardy space of real-rational transfer function matrices.
Hardy space of real-rational transfer function matrices.
The ith eigenvalue of G.