On the Strong Solutions and Maximal Solutions of Generalized Algebraic Riccati Equations

Improving the Accuracy of the Solutions of Riccati Equations

Maximal and Stabilizing Hermitian Solutions for Discrete-Time Coupled Algebraic Riccati Equations

Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and -control of Markovian jump linear systems are considered. First, the L_ equations that arise from the quadratic optimal control problem are studied. The matrix cost is only assumed to be hermitian. Conditions for existence of the maximal hermitian solution are derived in terms of the concept of mean sq...

Strong Convergence and Convergence Rates of Approximating Solutions for Algebraic Riccati Equations in Hilbert Spaces*

Inthis paper, -we considersthe linear quadratic optimal control 4, problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces. The optimal control is given by a feedback form in terms of solution r1 to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence rl of finite dimensional approximations of the solution ...

Structure-preserving algorithms for Hermitian solutions of algebraic Riccati equations

In this paper, we propose structure-preserving algorithms for the computation of Hermitian solutions of continuous/discrete-time algebraic Riccati equations. Under assumptions that partial multiplicities of purely imaging and unimodular eigenvalues (if any) of the associated Hamiltonian and symplectic pencil, respectively, are all even, we prove that the developed structure-preserving algorithm...

Accurate solutions of M-matrix algebraic Riccati equations

This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic Riccati Equations (MARE) XDX −AX −XB + C = 0 by which we mean the following conformally partitioned matrix ( B −D −C A ) is a nonsingular or an irreducible singular M -matrix. It is known that such an MARE has a unique minimal nonnegative solution Φ. ...