 
Summary: 1
Homogeneous Polynomial Forms for
Simultaneous Stabilizability of Families of
Linear Control Systems: a Tensor Product
Approach
Claudio Altafini
SISSAISAS, International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
altafini@sissa.it
keyword: Tensor Product, Homogeneous Polynomial Forms, Common Lyapunov Functions, Robust
Stabilizability.
Abstract
The paper uses the formalism of tensor products in order to deal with the problem of simultaneous
stabilizability of a family of linear control systems by means of Lyapunov functions which are homoge
neous polynomial forms. While the feedback synthesis seems to be nonconvex, the simultaneous stability
by means of homogeneous polynomial forms of the uncontrollable modes yields (convex) necessary but
not sufficient conditions for simultaneous stabilizability.
I. INTRODUCTION
For a linear system without inputs, an time tensor product of its ndimensional state space yields
a polynomial system homogeneous of degree . See [5] for a survey of the use of tensor products
