This paper is concerned with rational matrix equations occuring in stochastic control that play an analogous role as the algebraic Riccati equation does in deterministic control. We will therefore sometimes refer to these equations as stochastic (algebraic) Riccati equations. A first rigorous treatment of a stochastic Riccati equation from LQ-control theory seems to have been undertaken by Wonh...

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a flat bottom. T...

An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic differential game is considered. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in the payoff/cost functional are not assumed to be definite/nonsingular, and the cross-terms between two controls are allowed to appear. A forward-backward s...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...

We study the problem of strongly coprime factorization over H-infinity of the unit disc. We give a necessary and sufficient condition for the existence of such a coprime factorization in terms of an optimal control problem over the doubly infinite discrete-time axis. In particular, we show that an equivalent condition for the existence of such a coprime factorization is that both the control an...

A method for H∞ observer design for linear time-delay systems based on the algebraic Riccati equation is proposed. A ”weak” sufficient condition for the existence of such an observer is given.

The paper describes the set of solutions of the discrete-time algebraic Riccati equation. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix of an unmixed solution. The results of the paper provide an extended counterpart of the parametrization theory of...

*Correspondence: [email protected] 1Department of Mathematical Sciences, University of Karachi, Karachi, 75270, Pakistan Full list of author information is available at the end of the article Abstract The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has ...

Abstract The fractional wave equation is presented as a generalization of the wave equation when arbitrary fractional order derivatives are involved. We have considered variable dielectric environments for the wave propagation phenomena. The Jumarie’s modified Riemann-Liouville derivative has been introduced and the solutions of the fractional Riccati differential equation have been applied to ...

To construct exact solutions of nonlinear partial differential equation, a multiple Riccati equations rational expansion method (MRERE) is presented and a series of novel solutions of the Broer–Kaup–Kupershmidt system are found. The novel solutions obtained by MRERE method include solutions of hyperbolic (solitary) function and triangular periodic functions appearing at the same time. 2005 Else...