On flat systems behaviors and observable image representations

In this short paper we propose a definition of flatness for systems not necessarily given in input/state/output representation. A flat system is a system for which there exists a mapping such that the manifest system behavior is equal to the image of this mapping, and such that the latent variable appearing in this image representation can be written as a function of the manifest variable and its derivatives up to some order. For linear differential systems, flatness is equivalent to controllability. We will generalize the main theorem to general linear differential systems.

Dissipativity preserving model reduction by retention of trajectories of minimal dissipation

We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas (Syst Control Lett 54:361-374, 2005) and Sorensen (Syst Control Lett 54:347-360, 2005) is shown to be a particular case of this more general class of model reduction procedures

Sampled-data and discrete-time H2H_2 optimal control

This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This discrete-time H2 problem is always singular. Motivated by this, in this paper we give a treatment of the discrete-time H2 optimal control problem in its full generality. The results we obtain are then applied to the singular discrete-time H2 problem arising from the sampled-data H2 problem. In particular, we give conditions for the existence of optimal sampled data controllers. We also show that the H2 performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, we show that the optimal sampled-data H2 performance converges to the continuous-time optimal H2 performance as the sampling period converges to zero

Linear quadratic problems with indefinite cost for discrete time systems

This paper deals with the discrete-time infinite-horizon linear quadratic problem with indefinite cost criterion. Given a discrete-time linear system, an indefinite cost-functional and a linear subspace of the state space, we consider the problem of minimizing the cost-functional over all inputs that force the state trajectory to converge to the given subspace. We give a geometric characterization of the set of all hermitian solutions of the discrete-time algebraic Riccati equation. This characterization forms the discrete-time counterpart of the well-known geometric characterization of the set of all real symmetric solutions of the continuous-time algebraic Riccati equation as developed by Willems [IEEE Trans. Automat. Control, 16 (1971), pp. 621- 634] and Coppel [Bull. Austral. Math. Soc., 10 (1974), pp. 377-401]. In the set of all hermitian solutions of the Riccati equation we identify the solution that leads to the optimal cost for the above mentioned linear quadratic problem. Finally, we give necessary and sufficient conditions for the existence of optimal controls. Keywords: Discrete time optimal control, indefinite cost, algebraic Riccati equation, linear endpoint constraints