Giovanni Marro

Controlled and conditioned invariant subspaces in linear system theory

The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems. In this paper, we definecontrolled andconditioned invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems. Moreover, we prove some fundamental theorems on which the computation of the above-mentioned subspaces is based. Then, we give two examples of practical application of the previous concepts concerning the determination of the constant output and perfect output controllability subspaces.

On the observability of linear, time-invariant systems with unknown inputs

This paper considers the observation of linear, time-invariant dynamical systems in the general case in which some of the input functions are unknown. By arguments based on the concepts of controlled and conditioned invariance, a convenient expression for the observability subspace is found which includes the well-known expression for the case in which the input functions are given.

On the robust controlled invariant

Abstract The robust controlled invariant is defined as a tool to characterize systems subject to parameter changes and to set up a geometric approach to robustness in the large in multi-variable control problems. As a typical application, the robust disturbance decoupling problem, an extended version of the well-known disturbance decoupling, is presented and a necessary and sufficient condition for it to have a solution is derived.

Self-bounded controlled invariant subspaces: A straightforward approach to constrained controllability

AbstractA lattice-type structure is shown to exist in a particular subset of the set of all (A, ℱ)-controlled invariants contained in

On Wonham stabilizability condition in the synthesis of observers for unknown-input systems

\mathcal{N}

Geometric insight into discrete-time cheap and singular linear quadratic Riccati (LQR) problems

and containing

Unknown-state, unknown-input reconstruction in discrete-time nonminimum-phase systems: Geometric methods

\mathcal{N}