André M. de Oliveira†, Oswaldo L. V. Costa‡
Abstract: In this chapter we discuss the H2 control for Markov jump linear systems in a context of partial observation of both the Markov chain and the state variable. The controller is static and depends on an observed variable that provides the only information of the Markov
variable in a context of hidden Markov chains. We propose a new design condition in terms of linear matrix inequalities considering rank constraints in suitable system matrices that are easily fulfilled. Next we investigate the case in which the detector provides perfect estimations
of the Markov chain and all the states are available to the controller. Finally we compare this result with the so-called two-step procedure for hidden Markov jump linear systems in an academic example of asystem subject to faults.
MSC: 93C05, 93C55, 93E20, 60J10, 93E25
keywords: Stochastic control; H2 control; static output feedback control; Markov processes; linear matrix inequalities
DOI 10.56082/annalsarscimath.2020.1-2.405
†andre.marcorin@unifesp.br Institute of Science and Technology, Federal University of Sa˜o Paulo (UNIFESP), Av. Cesare Mansueto Giulio Lattes, 1201 – Eugˆenio de Mello, Sa˜o Jos´e dos Campos, SP, CEP: 12247-014, Brazil. Paper written with financial support of the
National Council for Scientific and Technological Development grants CNPq-304149/2019-5; the FAPESP/Shell through the Research Center for Gas Innovation grant FAPESP/Shell2014/50279-4; the project INCT, grants CNPq/INCT-465755/2014-3 and FAPESP/INCT2014/50851-0; and the Coordena¸c˜ao de Aperfei¸coamento de Pessoal de N´ıvel Superior – CAPES, Finance Code 88887.136349/2017-00.
‡Departamento de Engenharia de Telecomunica¸c˜oes e Controle, Escola Polit´ecnica na Universidade de S˜ao Paulo (EPUSP), Avenida Professor Luciano Gualberto, trav. 3, n. 158, Sa˜o Paulo, SP, CEP: 05508-010, Brazil.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
