We consider the classic problem of minimizing a quadratic cost functional for well-posed linear systems over the class of inputs that are square integrable and that produce a square integrable output. As is well-known, the minimum cost can be expressed in terms of a bounded nonnegative selfadjoint operator X that in the finite-dimensional case satisfies a Riccati equation. Unfortunately, the in...

Some global existence criteria for quaternionic Riccati equations are established. Two of them used to prove a completely non conjugation theorem solutions linear systems ordinary differential equations.

Discrete algebraic Riccati equations and their fixed points are well understood arise in a variety of applications; however, the time-varying have not yet been fully explored literature. In this article we provide self-contained study discrete time matrix difference equations. particular, novel semigroup duality formula new Floquet-type representation for these Due to aperiodicity underlying fl...

This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation...