In this paper we investigate the closed-loop performance of a sampled-data control system by utilizing exact discretization techniques. In particular, for an H2 performance measure we give exact expressions for the closed-loop cost for a given sample interval h. After applying discrete-time LQG synthesis to the sampled-data system, the achievable performance is evaluated for fast sampling near ...

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...

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.

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and deterministic. The purpose of this pape...

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...

A new backward stable, structure preserving method of complexity O(n) is presented for computing the stable invariant subspace of a real Hamiltonian matrix and the stabilizing solution of the continuous-time algebraic Riccati equation. The new method is based on the relationship between the invariant subspaces of the Hamiltonian matrix H and the extended matrix [ 0 H H 0 ] and makes use of the ...

This paper deals with the discrete-time infinite-horizon linear quadratic problem with indefinite cost criterion. Given a discrete-time linear system, an indefinite costfunctional and a linear subspace of the state space, we consider the problem of minimizing the costfunctional over all inputs that force the state trajectory to converge to the given subspace. We give a geometric characterizatio...