Generic eigenvalue assignment by memoryless real output feedback

By extensive use of methods from algebraic geometry, X. Wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states, m inputs, and p outputs, if n < mp. Here we show the same result using no more of algebraic geometry than the definition of genericity

A behavioral approach to singular systems

The notion of behaviors introduced by Willems gives a good description of dynamical systems without reference to any particular representation of the system in terms of equations. In this note, we introduce a notion of behaviors that allows us to describe singular systems in a very natural way. The new definition of behaviors given here is closely related to that of a sheaf over the projective line, and we make this connection precise

A behavioral approach to singular systems

The notion of behaviors introduced by Willems gives a good description of dynamical systems without reference to any particular representation of the system in terms of equations. In this note, we introduce a notion of behaviors that allows us to describe singular systems in a very natural way. The new definition of behaviors given here is closely related to that of a sheaf over the projective line, and we make this connection precise

Realization by inspection

We investigate which first-order representations can be obtained from high-order representations of linear systems `by inspection', that is just by rearrangement of the data. Under quite weak conditions it is possible to obtain minimal realizations in the so-called pencil form; under stronger conditions one can obtain minimal realizations in standard state space form by inspection. The development is based on a reformulation of the realization problem as a problem of finding a complete set of basis vectors for the nullspace of a given constant matrix. Since no numerical computation is needed, the realization method is in particular suitable for situations in which some of the coefficients are symbolic rather than numerical

Generic eigenvalue assignment by memoryless real output feedback

By extensive use of methods from algebraic geometry, X. Wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with $n$ states, $m$ inputs, and $p$ outputs, if $