Zeros at Infinity for Infinite Dimensional Systems

M Malabre (1) , Rabah Rabah (1)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

The concept of zeros at infinity is generalized to some particular cases of infinite dimensional control systems : those described with bounded operators and having a finite number of inputs and outputs. These zeros are characterized with the help of four equivalent descriptions. Two geometric characterizations are provided as well as a matricial one using some particular Toeplitz matrices. The last one is directly deduced from the Structure Algorithm. Finally, for systems having a finite number of disturbance inputs, we show that the Disturbance Decoupling Problem with Measurement of the Disturbance is solvable if and only if the orders of the zeros at infinity are the same for the system with and without the disturbance. Applications to invertibility tests or to ideal observability are also given.

Domaines: Optimisation et contrôle [math.OC]

M Malabre, Rabah Rabah. Zeros at Infinity for Infinite Dimensional Systems. Realization and Modelling in System Theory, 3, , pp.199 - 206, 1990, Progress in Systems and Control Theory 978-1-4612-8033-0. ⟨10.1007/978-1-4612-3462-3_21⟩. ⟨hal-01419626⟩