In this short paper we study the existence of positive and negative semide nite solutions of the algebraic Riccati equation corresponding to linear quadratic problems with an inde nite cost functional. An important role is played by certain two-variable polynomial matrices associated with the algebraic Riccati equation. We characterize al unmixed solutions in terms of the Pick matrices associat...

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BS...

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...

This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of systems. There two main contributions: (1) To best authors' knowledge, present is first to establish necessary sufficient solvability condition this kind problem derive analytical form an controller through overcoming obstacle that separ...