In this paper an infinite-dimensional LQR control-based design for a system containing linear hyperbolic partial differential equations coupled with linear ordinary differential equations is presented. The design is based on an infinite-dimensional Hilbert state-space representation of the coupled system. The feedback control gain is obtained by solving algebraic and differential matrix Riccati...

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equat...

We consider the linear quadratic differential games for positive linear systems with the feedback information structure and two players. The Newton method to obtain the stabilizing solution of a corresponding set of Riccati equations is presented in the literature. Here, we modify the Newton method and propose a new faster iterative method. Moreover, the convergence properties of the modificati...

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

Abstract. The asymptotic behaviour for solutions of a difference equation ∆zn = f(n, zn), where the complex-valued function f(n, z) is in some meaning close to a holomorphic function h, and of a Riccati difference equation is studied using a Lyapunov function method. The paper is motivated by papers on the asymptotic behaviour of the solutions of differential equations with complex-valued right...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

A new parametrization of the Eilenberger equations of superconductivity in terms of the solutions to a scalar differential equation of the Riccati type is introduced. It is shown that the quasiclassical propagator, and in particular the local density of states, may be reconstructed, without explicit knowledge of any eigenfunctions and eigenvalues, by solving a simple initial value problem for t...

Let u be a hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F , zAF ′ = BF +CF +D and a distributional equation for u, D(Au) = B1u + C1u+H1L, where L is the Lebesgue functional, and the polynomials B1, C1,D1 are define...

In this article, a hybrid numerical technique combining the Laplace transform and residual power series method is used to construct solution of nonlinear fractional Riccati differential equation in sense Caputo derivative. The proposed implemented analytical solutions target equation. tested for eminent examples obtained results demonstrate accuracy efficiency by comparing it with other methods.