We study large‐scale, continuous‐time linear time‐invariant control systems with a sparse or
structured state matrix and a relatively small number of inputs and outputs. The main …

In previous papers, a class of hierarchical matrices (ℋ-matrices) is introduced which are data-
sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we …

In this paper we propose a new projection method to solve large-scale continuous-time
Lyapunov matrix equations. The new approach projects the problem onto a much smaller …

We propose a new framework based on optimization on manifolds to approximate the
solution of a Lyapunov matrix equation by a low-rank matrix. The method minimizes the error …

A few methods are proposed for solving large Lyapunov equations that arise in control
problems. The common case where the right hand side is a small rank matrix is considered …

Efficient numerical algorithms for the solution of large and sparse matrix Riccati and
Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have …

In this work we address the issue of integrating symmetric Riccati and Lyapunov matrix
differential equations. In many cases--typical in applications--the solutions are positive …

In this paper a new algorithm for solving algebraic Riccati equations (both continuous-time
and discrete-time versions) is presented. The method studied is a variant of the classical …

A hybrid method for computing the feedback gains in linear quadratic regulator problems is
proposed. The method, which combines use of a Chandrasekhar type system with an …

In this paper, we study possible low rank solution methods for generalized Lyapunov
equations arising in bilinear and stochastic control. We show that under certain assumptions …