In this paper, we present a naturally numerical method for finding the maximal hermitian solution X+ of the Discrete-Time Algebraic Riccati Equation (DTARE) based on the convergence of a monotone sequence of hermitian matrices. MIRAMARE TRIESTE August 1999 E-mail: [email protected] 227 Nguyen Van Cu, Q5, HCMC, Vietnam.

The aim of this paper is to examine a numerical method for the computation of approximate solution of the continuous-time algebraic Riccati equation using Krylov subspace matrix. First of all, Global Arnoldi process is initiated to construct an orthonormal basis. In addition, Krylov subspace matrix is employed as projection method because it is one of the frequently referred method in the liter...

where A,B and C are complex matrices of dimensions n × n, n × p and q × n respectively. We focus on the set T = {X | R(X) = 0, X ≤ 0} of negative-semidefinite solutions and we shall characterize those elementsX of T which are isolated (in the topology which T inherits as a subset of the normed space C n×n). Such an isolated X has the property that for a sufficiently small there is no solution Y...

Abstract: In the present paper we obtain a closed-form solution for the class of discrete-time algebraic Riccati equations (DTARE), whenever the eigenvalues of the A matrix are distinct. The obtained closed-form solution gives insight on issues such as loss of controllability and it might also prove comparable in terms of numerical precision over current solving algorithms. We also consider fur...

Abstract: In this paper, we derive the analytical closed form solution of a class of Riccati equations. Since it is well known that to every Riccati equation there corresponds a linear homogeneous ordinary differential equation (ODE), the result obtained is subsequently employed to derive the analytical solution of the class of second order linear homogeneous ODEs corresponding to the class of ...

The aim of this work is to obtain optimal-order error estimates for the LQR (Linear-quadratic regulator) problem in a strongly damped 1-D wave equation. We consider a finite element discretization of the system dynamics and a control law constant in the spatial dimension, which is studied in both point and distributed case. To solve the LQR problem, we seek a feedback control which depends on 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 ...

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...