Finite‐region stabilization via dynamic output feedback for 2‐D Roesser models

Abstract

Finite‐region stability (FRS), a generalization of finite‐time stability, has been used to analyze the transient behavior of discrete two‐dimensional (2‐D) systems. In this paper, we consider the problem of FRS for discrete 2‐D Roesser models via dynamic output feedback. First, a sufficient condition is given to design the dynamic output feedback controller with a state feedback‐observer structure, which ensures the closed‐loop system FRS. Then, this condition is reducible to a condition that is solvable by linear matrix inequalities. Finally, viable experimental results are demonstrated by an illustrative example.

Output tracking control for 2‐D discrete systems with actuator failures

“…According to the Schur complement, condition (22) is equivalent to inequality (20). The proof is completed.…”

“…Theorems 2 and 3 present the reliable H ∞ tracking controller design conditions based on LMIs, which can be effectively solved via LMI control toolbox. 36 The controller gains can be obtained by solving the LMI (17) for known actuator failure parameter or LMI (20) for unknown actuator failure parameter. In addition, by solving the following optimization problem ((23) for Theorem 2 and (24) for Theorem 3):…”

“…min 𝛾 2 subject to (20), (24) we can obtain a desired H ∞ controller such that the H ∞ tracking performance index 𝛾 of the augmented closed-loop system is minimized.…”

“…Recently, the stabilization and control problem for 2‐D systems have attracted considerable research attention, and many important results have been reported in the literature. To mention a few, in Reference 20, the finite‐region stabilization problem for discrete 2‐D systems via dynamic output feedback has been considered. In Reference 21, the problem of sliding mode control for uncertain 2‐D delayed systems with uncertainties and nonlinearities has been solved.…”