Media type: E-Article Title: Output‐based H2 optimal controllers for a class of discrete‐time stochastic linear systems with periodic coefficients Contributor: Dragan, Vasile; Morozan, Toader; Stoica, Adrian‐Mihail Published: Wiley, 2015 Published in: International Journal of Robust and Nonlinear Control, 25 (2015) 13, Seite 1897-1926 Language: English DOI: 10.1002/rnc.3173 ISSN: 1049-8923; 1099-1239 Keywords: Electrical and Electronic Engineering ; Industrial and Manufacturing Engineering ; Mechanical Engineering ; Aerospace Engineering ; Biomedical Engineering ; General Chemical Engineering ; Control and Systems Engineering Origination: Footnote: Description: <jats:title>Summary</jats:title><jats:p>The aim of the paper is to present a design procedure of the optimal controller minimizing the <jats:italic>H</jats:italic><jats:sub>2</jats:sub>‐type norm of discrete‐time stochastic linear systems with periodic coefficients simultaneously affected by a nonhomogeneous but periodic Markov chain and state and control multiplicative white noise perturbations. Firstly, two <jats:italic>H</jats:italic><jats:sub>2</jats:sub>‐type norms for the linear stochastic systems under consideration were introduced. These <jats:italic>H</jats:italic><jats:sub>2</jats:sub>‐type norms may be viewed as measures of the effect of the additive white noise perturbations on the regulated output of the considered system. Before deriving of the state space representation of the optimal controller, some useful formulae of the two <jats:italic>H</jats:italic><jats:sub>2</jats:sub>‐type norms were obtained. These formulae are expressed in terms of periodic solutions of some suitable linear equations and are derived in the absence of some additional assumptions regarding the Markov chain other than the periodicity of the sequence of the transition probability matrices. Further, it is shown that the optimal <jats:italic>H</jats:italic><jats:sub>2</jats:sub> controller depends on the stabilizing solutions of some specific systems of coupled Riccati equations, which generalize the well‐known control and filtering equations from linear time invariant case. For the readers convenience, the paper presents iterative numerical algorithms for the computations of the stabilizing solutions of these Riccati type systems. The theoretical developments are illustrated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.</jats:p>