Quadratic and H-infinity switching control for discrete-time linear systems with multiplicative noises

Autor(es)

Costa, O. L. V. ^[1] ; Gonzaga, C. A. C. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Escola Politecn, Dept Engn Telecomunicacoes & Controle, BR-05508900 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: International Journal of Control; v. 87, n. 11, p. 2312-2326, 2014.
• Citações Web of Science: 2

Resumo

The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H-infinity criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov-Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov-Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov-Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H-infinity performance costs are bounded above by a constant value. These results are illustrated with some numerical examples. (AU)

• Processo FAPESP: 12/17188-0 - Estabilidade e desempenho de uma classe de sistemas não-lineares a saltos markovianos em tempo discreto
• Beneficiário: Carlos Alberto Cavichioli Gonzaga
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado