Optimal generalized sampled-data hold functions with a constrained structure

This paper deals with the optimal control of a continuous-time system using a structurally constrained generalized sampled-data hold function (GSHF). It is assumed that a stabilizing GSHF with a desired structure exists for the system. This desired structure is defined by a set of basis functions, and the GSHF is given as a weighted sum of these basis functions. The main objective of this paper is to adjust the coefficients of the weighted sum in order to minimize a predefined continuous-time LQR performance index, which accounts for the intersample ripple. This implies that the resultant GSHF has the same structure as the original one, while it minimizes the intersample ripple effect. The proposed method uses the recent developments in semidefinite programming to tune the parameters of the GSHF