  In this paper, we study the problem of identifying the impulse response of a
linear time invariant (LTI) dynamical system from the knowledge of the input
signal and a finite set of noisy output observations. We adopt an approach
based on regularization in a Reproducing Kernel Hilbert Space (RKHS) that takes
into account both continuous and discrete time systems. The focus of the paper
is on designing spaces that are well suited for temporal impulse response
modeling. To this end, we construct and characterize general families of
kernels that incorporate system properties such as stability, relative degree,
absence of oscillatory behavior, smoothness, or delay. In addition, we discuss
the possibility of automatically searching over these classes by means of
kernel learning techniques, so as to capture different modes of the system to
be identified.
