Using the idea of the very recently generalized Kudryashov method and based on a generalized Riccati equation we present an alternative method which can be considered as an extension of the well known tanh method. As application of the proposed method, we obtain exact solutions of the Dispersive modified Benjamin-Bona-Mahony equation showing in this way its effectiveness. Mathematics Subject Cl...

Let R be a commutative complex unital semisimple Banach algebra with the involution ·⋆. Sufficient conditions are given for the existence of a stabilizing solution to the H ∞ Riccati equation when the matricial data has entries from R. Applications to spatially distributed systems are discussed.

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

The paper deals with the associated algebraic matrix Riccati equation (AAMRE), closely related to the standard algebraic matrix Riccati equation arising in the theory of linear-quadratic optimisation and filtering. The sensitivity of the AAMRE relative to perturbations in its coefficients is studied. Both linear local (norm-wise and componentwise) and non-linear non-local perturbation bounds ar...

In this paper we present a Nash equilibrium problem of linear quadratic zero-sum dynamic games for descriptor system. We assume that the players give a linear feedback to the game. For the game with finite planning horizon we derive a differential Riccati type equation. For the game with infinite planning horizon we consider an algebraic Riccati type equation. The connection of the game solutio...

Ten new exact solutions of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y are presented. The solutions are obtained by assuming certain relations among the coefficients a(x), b(x) and c(x) of the Riccati equation, in the form of some integral or differential expressions, also involving some arbitrary functions. By appropriately choosing the form of the coefficients of the Riccati equation, w...

In this paper, using modified FF-expansion method, we present some explicit formulas of exact traveling wave solutions for the foam drainage equation. A modified FF-expansion method is proposed by taking full advantages of FF-expansion method and Riccati equation in seeking exact solutions of non-linear partial differential equations.

A generalized Chebyshev wavelet operational matrix (CWOM) is presented for the solution of nonlinear Riccati differential equations. The operational matrix together with suitable collocation points converts the fractional order Riccati differential equations into a system of algebraic equations. Accuracy and efficiency of the proposed method is verified through numerical examples and comparison...

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.