Input-Output Finite-Time Stabilization of Linear Time-Varying Discrete-Time Systems

• 成果类型: Article
• 署名作者: Amato, Francesco; Cosentino, Carlo; De Tommasi, Gianmaria; Pironti, Alfredo; Romano, Maria
• 署名单位: University of Naples Federico II; Magna Graecia University of Catanzaro
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3161374
• 发表日期: 2022
• 页码: 4438-4450
• 关键词: Discrete-time systems; Sufficient conditions; stability analysis; optimization; Numerical stability; Closed loop systems; Linear systems; Controller design; input-output finite-time stability (IO-FTS); linear discrete-time systems; LMI

摘要

This article deals with the input-output finite-time stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite-interval of time; therefore, the development and application of finite-time control methodologies is of particular relevance. The first contribution of this article is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of generalized difference Lyapunov equations; the latter allows one to establish the feasibility of an optimization problem by solving a set of difference linear matrix inequalities (DLMIs). The second contribution of this article is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example.