Disturbance Decoupling for Polynomial Systems

We study nonlinear control systems x˙(t) = f(x(t)) + g(x(t))u(t) + d(x(t))w(t), y(t) = h(x(t)), where f,g,d,h are polynomial functions. The output y is called decouplable from disturbances if there exists a polynomial state feedback u(t) = α(x(t)) + β(x(t))v(t) with β as an invertible matrix, which renders the output y invariant under disturbances. The question whether this is possible leads to the concept of controlled invariant modules. We give algebraic characterisations to decide whether an output is invariant or decouplable and present algorithms to constructively verify these criteria by symbolic computational methods.