Displaying similar documents to “Sixty years of cybernetics: a comparison of approaches to solving the H 2 control problem”

Idempotent versions of Haar’s Lemma: links between comparison of discrete event systems with different state spaces and control

Mourad Ahmane, Laurent Truffet (2007)

Kybernetika

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Haar's Lemma (1918) deals with the algebraic characterization of the inclusion of polyhedral sets. This Lemma has been involved many times in automatic control of linear dynamical systems via positive invariance of polyhedrons. More recently, it has been used to characterize stochastic comparison w.r.t. linear/integral ordering of Markov (reward) chains. In this paper we develop a state space oriented approach to the control of Discrete Event Systems (DES) based on the remark that most...

SPR0 substitutions and families of algebraic Riccati equations

G. Fernández-Anaya, J. C. Martínez García, Vladimír Kučera, D. Aguilar George (2006)

Kybernetika

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We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in H ∞ -norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated H ∞ -norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated...