The existence and uniqueness of solutions for kernel-based system identification

The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In resulting framework, impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting stable responses. consequent well-defined under central assumption that convolution operators restricted to are continuous linear functionals. Moreover, according this assumption, representer theorem hold, and therefore, can be estimated by solving finite-dimensional program. Thus, continuity feature plays significant role kernel-based identification. We show guaranteed satisfied considerably general situations, namely when input signal bounded, integrable function, case continuous-time dynamics, continuous. Furthermore, strong convexity property imply admits unique solution. Consequently, it follows approach.