 
Summary: Bilinear Control Systems: Theory and Applications
Instructor: Claudio Altafini, SISSA (Int. School for Advanced Studies), Trieste. email: altafini@sissa.it
Aim: Bilinear Systems are an important class of nonlinear control systems. The course aims at
giving an overview of the main control problems and of some of the mathematical tools (notably
differential geometric and Lie algebraic methods) required in the study of bilinear control systems.
Topics:
1. Introductory material
· manifolds, vector fields, tangent spaces;
· orbits of vector fields and Frobenius Theorem;
· controllablity and Chow Theorem;
· drift versus driftless systems, accessibility versus controllability;
2. Bilinear control systems
· bilinear systems and matrix transition Lie groups;
· structure of matrix Lie groups (homogeneous spaces, transitivity, exponential map and
canonical coordinates);
· Lie algebras (Levi decomposition, semisimpicity, solvability, nilpotency, Cartan criteria);
· controllability properties for bilinear control systems on matrix Lie groups;
3. Control methods
· feedback linearization;
· system inversion and differential flatness;
