Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

Abstract

This paper investigates the asymptotic stabilization of the 2-D continuous-discrete-time systems via dynamic output feedback. The problem is formulated in a general framework, where the system and controller are both described by the Roesser model. By rigorous mathematical works, a linear matrix inequality (LMI) condition is established to ensure the asymptotic stability of the closed-loop system. Using this LMI condition, the problem of determining the stabilizing controller parameters is converted to a rank minimization problem (RMP) with an LMI constraint, or equivalently to a rank-constrained optimization problem (RCOP). When this RMP (or equivalently this RCOP) has a solution, then the controller parameters are obtained uniquely by an explicit formula in terms of this solution. Moreover, it is shown that one can transform the problem of one-dimensional continuous-time iterative learning control (ILC) design to a 2-D stabilization problem, and consequently solve it using the presented two-dimensional scheme. Some numerical examples are given to illustrate the proposed method.