The initial value problem for a matrix Riccati differential equation associated with an M -matrix is known to have a global solution X(t) on [0,∞) when X(0) takes values from a suitable set of nonnegative matrices. It is also known, except for the critical case, that as t goes to infinity X(t) converges to the minimal nonnegative solution of the corresponding algebraic Riccati equation. In this...

In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, darkand Peregrine-type soliton solutio...

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). Then the closed-loop optimal strategies are given by u(t) = −R−1B∗P(t,x(t)), v(t) = −S−1C∗P(t,x(t)). For differential game problems of...

The algorithm of solution of discrete periodic Riccati equation which arises, in particular, in problems of synthesis of system of stabilization of the hopping robot is offered. In this algorithm it is removed a number of restrictions on matrix coefficients of the equation which are peculiar to existing algorithms. It is essential, that this algorithm allows to use at the realization of procedu...