Dirichlet series solutions of generalized Riccati equations

Improving the Accuracy of the Solutions of Riccati Equations

Generalized Solutions of Riccati Equalities and Inequalities

In this talk we present the Riccati inequality and equality for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results are based on earlier work on the Kalman-Yakubovich-Popov inequality in [AKP1]. The main theorems are closely related to the results of Yu.M. Arlinskĭı [ARL]. The main difference is that we do not assume the original ...

Approximation of Solutions of Riccati Equations

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. The theory of exponentially dichotomous operators and bisemigroups is instrumental in our approach.

Generalized Riccati Equations Arising in Stochastic Games

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and deterministic. The purpose of this pape...

Generalized power series solutions to linear partial differential equations

Let Θ = C[e−x1 , . . . , e−xn ][∂1, . . . , ∂n] and S = C[x1, . . . , xn][[eCx1+···+Cxn ]], where C is an effective field and xN 1 · · · x N n e Cx1+···+Cxn and S are given a suitable asymptotic ordering 4. Consider the mapping L : S → Sl ; f 7→ (L1 f, . . . , Ll f ), where L1, . . . , Ll ∈ Θ . For g = (g1, . . . , gl ) ∈ Sl L = im L , it is natural to ask how to solve the system L f = g. In th...