Abstract
In this paper we consider the problem ofL 1 sensitivity minimization for linear plants with commensurate input delays. We describe a procedure for computing the minimum performance, and we characterize optimal solutions. The computations involve solving a one-parameter family of finite-dimensional linear programs. Explicit solutions are presented for important special cases.
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Abbreviations
- X * :
-
Dual space of a normed linear spaceX
- \(\overline {BS} \) :
-
All elements inS with norm ≤ 1
- S ⊥ :
-
The annihilator subspace defined as\(\left\{ {x^* \in X^* |\left\langle {s,x^* } \right\rangle = 0 for all s \in S \subset X} \right\}\).
- ⊥ S :
-
The annihilator subspace defined as\(\left\{ {x \in X|\left\langle {s,x} \right\rangle = 0 for all s \in S \subset X^* } \right\}\).
- BV(X):
-
Functions of bounded variation onX
- C 0(X):
-
Continuous function on a locally compact spaceX such that for all ɛ > 0, {x ε X¦ ¦f(x)¦ɛs is compact
- C N(a, b):
-
Vectors of continuous functions on (a, b)
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The authors acknowledge support from the Army Research Office, Center for Intelligent Control, under grant DAAL03-86-K-0171, and the National Science Foundation, under grant 8810178-ECS.
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Dahleh, M.A., Ohta, Y. L 1 Sensitivity minimization for plants with commensurate delays. Math. Control Signal Systems 5, 281–293 (1992). https://doi.org/10.1007/BF01211562
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DOI: https://doi.org/10.1007/BF01211562