Kernel approximation approach to the L1 analysis of sampled-data systems

This paper provides a method for the L₁ analysis of sampled-data systems, by which we mean the computation of their L_∞-induced norm. We first apply the lifting approach to sampled-data systems and derive an operator theoretic representation of their input/output relation. We then apply fast-lifting by which the sampling interval [0, h) is divided into M subintervals with an equal width, and provide methods for computing the L_∞-induced norm. Specifically, we use an idea of kernel approximation approach, in which the kernel function of an input operator and the hold function of an output operator are approximated by staircase or piecewise linear functions. Furthermore, it is shown that the approximation errors in staircase or piecewise linear approximation are ensured to be reciprocally proportional to M or M², respectively.