Backward error for the discrete-time algebraic Riccati equation

An efficient algorithm for the discrete-time algebraic Riccati equation

In this paper the authors develop a new algorithm to solve the standard discrete-time algebraic Riccati equation by using a skewHamiltonian transformation and the square-root method. The algorithm is structure-preserving and efficient because the Hamiltonian structure is fully exploited and only orthogonal transformations are used. The efficiency and stability of the algorithm are analyzed. Num...

Backward Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation

Normwise backward errors and residual bounds for an approximate Hermitian positive semidefinite solution set to the periodic discrete-time algebraic Riccati equation are obtained. The results are illustrated by using simple numerical examples.

Intervals of solutions of the discrete-time algebraic Riccati equation

If two solutions Y ≤ Z of the DARE are given then the set of solutions X with Y ≤ X ≤ Z can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y . The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.

Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation

This paper is devoted to the perturbation analysis for the periodic discrete-time algebraic Riccati equations (P-DAREs). Perturbation bounds and condition numbers of the Hermitian positive semidefinite solution set to the P-DAREs are obtained. The results are illustrated by numerical examples.

Discrete Time H∞ Algebraic Riccati Equations