We consider the algebraic Riccati equation for which the four coefficient matrices form an M -matrix K. When K is a nonsingular M -matrix or an irreducible singular M -matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M ...

Abstract—In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be ...

The technique of space invariant embedding, applied to a second order boundary value problem defined in a cylindrical domain, gives rise to a system of uncoupled first order initial value problems that includes a nonlinear Riccati equation on a unbounded functional operator. We present a method to justify this equation that uses a parabolic regularization of the original problem.

We consider a nonlinear time fractional partial differential equation with forced term subject to the Neumann boundary condition. Several sufficient conditions are established for oscillation of solutions of such equation by using the integral averaging method and a generalized Riccati technique. The main results are illustrated by examples. 2014 Elsevier Inc. All rights reserved.

Generating quasi-isospectral potentials by the methods of supersymmetric quantum mechanics (SUSYQM) is a simple and well-known mathematical technique [1]. Its relationships with intertwining, factorization, Darboux covariance, and inverse scattering procedures have been recently reviewed by the author [2]. Also, the author, either in collaboration or alone [3] dealt extensively with a SUSYQM pr...

When Newton’s method is applied to find the maximal symmetric solution of a discrete algebraic Riccati equation (DARE), convergence can be guaranteed under moderate conditions. In particular, the initial guess does not need to be close to the solution. The convergence is quadratic if the Fréchet derivative is invertible at the solution. When the closed-loop matrix has eigenvalues on the unit ci...

Synchronization control of coupled continuous-time linear systems is studied. For identical systems that are stabilizable, a linear feedback law obtained via algebraic Riccati equation is shown to synchronize any fixed directed network of any number of coupled systems provided that the coupling is strong enough. The strength of coupling is determined by the smallest distance of a nonzero eigenv...