In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

By using majorization inequalities, we propose a new upper bound for summations of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation. The bound extends some of the previous results under certain conditions. Finally, we give a numerical example to illustrate the effectiveness of our results.

By using majorization inequalities, we propose a new upper bound for summations of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation. The bound extends some of the previous results under certain conditions. Finally, we give a numerical example to illustrate the effectiveness of our results.

In this paper we consider the generalized algebraic Riccati equation (GARE) for a continuous-time descriptor system. Necessary and sucient conditions for the existence of stabilizing solutions of the GARE are derived based on the Hamiltonian matrix pencil approach. A parametrization of all stabilizing solutions is also provided. The main result has a potential applicability to a wide class of ...

The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the discrete-time generalised Riccati equation, but, differently from the discrete case, to date the importance of this equation in the context of optimal contro...

We used what we called extended Fan’s sub-equation method and a new compound Riccati equations rational expansion method to construct the exact travelling wave solutions of the Davey-Stewartson DS equations. The basic idea of the proposed extended Fan’s subequation method is to take fulls advantage of the general elliptic equations, involving five parameters, which have many new solutions and w...

This paper presents a new characterization of stabilizability via Riccati equation for linear time-varying (LTV) systems. An equivalence is given between the global null-controllability, complete stabilizability and the existence of the solution of some appropriate Riccati differential equation.

We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equati...

The extended homogeneous balance method is used to construct exact traveling wave solutions of the Maccari system, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Maccari system equation are successfully obtained.

This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...