This paper studies Newton's method for solving the algebraic Riccati equation combined with an exact line search. Based on these considerations we present a Newton{like method for solving algebraic Riccati equations. This method can improve the sometimes erratic convergence behavior of Newton's method.

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross–coupled algebraic Riccati equations with a small positive parameter ε. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov equation direct method, to solve the cross–co...

The sensitivity of the discrete-time matrix Riccati equation relative to perturbations in its coefficients is studied. Both local and non-local perturbation bounds are obtained. In particular the conditioning of the equation is determined.

We introduce and prove some new interval oscillation criteria for a general class of forced second-order differential equations (E) : ( r(t)k1(x, x′) )′ + p(t)k2(x, x′)x′ + q(t)f(x) = e(t), t ≥ t0, where the functions k1(u, v), k2(u, v) and f(u) satisfy some general conditions. Our interval oscillation criteria and their proofs are different than previously published ones, and it is based on (i...

Abstract: This paper addresses a stability analysis problem and synthesis problem for pendulum-like systems with multiple nonlinearities. A method for analysing the Lagrange stability of a pendulum-like system with multiple nonlinearities is proposed. In order to study the synthesis problem, the paper develops an Extended Strict Bounded Real Lemma for unstable systems. A sufficient condition fo...

We consider the numerical solution of the continuous algebraic Riccati equation AX +XA−XFX +G = 0, with F = F , G = G of low rank and A large and sparse. We develop an algorithm for the low rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought after approximation can be obtained by a low rank update, in th...