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A Riccati Equation For Stochastic ... (1997)
BibTeX
@MISC{Hinrichsen97ariccati,
author = {D. Hinrichsen and A. J. Pritchard and Coventry Cv Al},
title = {A Riccati Equation For Stochastic ...},
year = {1997}
}
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Abstract
In this note we report on a new kind of algebraic Riccati equation which we encountered when studying an H 1 type problem of disturbance attenuation for stochastic linear systems. The same equation occurs in the analysis of stability radii of linear systems with both deterministic and stochastic uncertainties. The associated linear matrix inequality is also considered. 1 Introduction The objective of this paper is to introduce and discuss a new type of Riccati equation/inequality which we encountered when investigating an H 1 type problem of disturbance attenuation for a rather general class of stochastic linear systems. Consider systems \Sigma described by Ito stochastic differential equations of the form dx(t) = Ax(t)dt +A 0 x(t)dw 1 (t) +B 0 v(t)dw 2 (t) +B 1 v(t)dt +B 2 u(t)dt (1) z(t) = C 1 x(t) +D 11 v(t) +D 12 u(t) y(t) = C 2 x(t) +D 21 v(t); where w i ; i = 1; 2 are independent normalized scalar Wiener processes. Setting all the D's to zero and v = \Deltaz in (1) where ...
Keyphrases
riccati equation stochastic linear system disturbance attenuation type problem riccati equation inequality algebraic riccati equation new type ito stochastic differential equation associated linear matrix inequality form dx stability radius system sigma stochastic uncertainty linear system new kind general class independent normalized scalar wiener process
