We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuoustime algebraic Riccati equation A∗X + XA + Q = XGX, building on the work of [B. Hashemi, SCAN 2012] and adding several modifications to the Krawczyk procedure. Moreover, we describe a new O(n) direct method for verification, based on a fixed-point formulation of the e...

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by...

In this paper, asymmetric Algebraic Riccati Equations are analyzed. We derive a new parametrization of the set of solutions, which may be viewed as alternative to the classical one based on Lagrangian subspaces of a “pseudo-Hamiltonian” matrix. Generalizing the symmetric case, the proposed parametrization is given in terms of pairs of invariant subspaces of two related “feedback” matrices. Exte...

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 ...

In this paper, the dierential transform method (DTM) is applied to the Fisherequation. This method can be used to obtain the exact solutions of Fisherequation. Finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. These resultsshow that this technique is easy to apply.

We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(10). We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel...

Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...

A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons)in wronskian form are obtained using the method of Ablowitz and Satsuma. Also an extended class of rational solutions are found using an appropriate recursion relation. They are also solutions of Boussinesq equation and it is conjectured that t...

We survey theoretical properties and algorithms concerning the problem of solving a nonsymmetric algebraic Riccati equation, and we report on some known methods and new algorithmic advances. In particular, some results on the number of positive solutions are proved and a careful convergence analysis of Newton’s iteration is carried out in the cases of interest where some singularity conditions ...