This textbook offers theoretical, algorithmic and computational guidelines for solving the
most frequently encountered linear-quadratic optimization problems. It provides an overview …

The authors present analytical methods for synthesis of linear stationary and periodical
optimal controlled systems, and create effective computational algorithms for synthesis of …

In this tutorial paper, an overview is given of progress over the past ten to fifteen years
towards reliable and efficient numerical solution of various types of Riccati equations. Our …

Continuous-time algebraic Riccati equations (CAREs) can be transformed, à la Cayley, to
discrete-time algebraic Riccati equations (DAREs). The efficient structure-preserving …

Two collections of benchmark examples are presented for the numerical solution of
continuous-time and discrete-time algebraic Riccati equations. These collections may serve …

Scaling Riccati equations so that the solution has unit norm eliminates instabilities
associated with the inversion step of invariant-subspace-based (Schur) methods without …

The paper proposes a new computational approach with enhanced numerical robustness
for computing reduced order models of continuous systems by using the balanced stochastic …

Recent error bounds derived from the Schur method of solving algebraic Riccati equations
(ARE) complement residual error bounds associated with Newton refinement of approximate …

This article describes LAPACK-based Fortran 77 subroutines for the reduction of a
Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues …

The paper concerns with the computation with high accuracy of the nonnegative de nite
stabilizing solution of the matrix Riccati equation AT X+ XA+ XQX+ R= 0, where A is stable …