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Quadratic invariance is necessary and sufficient for convexity
 In American Control Conference
, 2011
"... In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of of Youla parameters. Previous work has shown that quadratic invariance of the controller set implies ..."
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Cited by 6 (1 self)
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In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of of Youla parameters. Previous work has shown that quadratic invariance of the controller set implies that the the set of Youla parameters is convex. In this short note, we prove the converse. We thereby show that the only decentralized control problems for which the set of Youla parameters is convex are those which are quadratically invariant. 1
An algebraic framework for quadratic invariance
 In IEEE Conference on Decision and Control
, 2010
"... In this paper, we present a general algebraic framework for analysing decentralized control systems. We consider systems defined by linear fractional functions over a commutative ring. This provides a general algebraic formulation and proof of the main results of quadratic invariance, as well as ..."
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In this paper, we present a general algebraic framework for analysing decentralized control systems. We consider systems defined by linear fractional functions over a commutative ring. This provides a general algebraic formulation and proof of the main results of quadratic invariance, as well as naturally covering rational multivariable systems, systems with delays, and multidimensional systems. The approach extends to the extended class of internally quadratically invariant systems. 1
Convexity of Decentralized Controller Synthesis
"... In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of Youla–Kucera parameters. Previous work has shown that quadratic invariance of the controller set imp ..."
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In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of Youla–Kucera parameters. Previous work has shown that quadratic invariance of the controller set implies that the set of Youla–Kucera parameters is convex. In this paper, we prove the converse. We thereby show that the only decentralized control problems for which the set of Youla–Kucera parameters is convex are those which are quadratically invariant. We further show that under additional assumptions, quadratic invariance is necessary and sufficient for the set of achievable closedloop maps to be convex. We give two versions of our results. The first applies to bounded linear operators on a Banach space and the second applies to (possibly unstable) causal LTI systems in discrete or continuous time. I