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.

Dynamic ILC for Linear Repetitive Processes Based on Different Relative Degrees

“…Based on discrete linear repetitive processes of actuator failure, the authors of [16,17] proposed a comprehensive design method of an integrated iterative learning fault-tolerant controller with state feedback and gave sufficient conditions for a closed-loop system to remain stable in the case of failure using Lyapunov stability theory. In [18,19], a P-type ILC algorithm was proposed for high relative linear multivariable discrete systems with iterative initial error.…”