On a rational matrix equation occuring in stochastic control

Author

Damm, T. ; Hinrichsen, D.

Author_Institution

Inst. for Dynamical Syst., Univ. of Bremen, Bremen, Germany

fYear

1999

fDate

Aug. 31 1999-Sept. 3 1999

Firstpage

3458

Lastpage

3463

Abstract

We regard a general class of rational matrix equations, which contains the continuous (CARE) and discrete (DARE) algebraic Riccati equations as special cases. Equations of this type were encountered in [EIIPSG] and [EHP98] where H^∞-type problems of disturbance attenuation for stochastic linear systems were studied. We develop a unifying framework for the analysis of these equations based on the theory of (resolvent) positive operators and show that they can be solved by Newton´s method starting at an arbitrary stabilizing matrix.

Keywords

Newton method; Riccati equations; linear systems; stability; stochastic systems; CARE; DARE; H∞-type problems; Newton method; continuous algebraic Riccati equations; discrete algebraic Riccati equations; disturbance attenuation; rational matrix equation; resolvent positive operators; stabilizing matrix; stochastic control; stochastic linear systems; Control theory; Linear matrix inequalities; Linear systems; Mathematical model; Newton method; Riccati equations; TV; Newton´s method; Riccati equations; concavity; resolvent positive operators; stochastic control;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ECC), 1999 European

Conference_Location

Karlsruhe

Print_ISBN

978-3-9524173-5-5

Type

conf

Filename

7099864