Algebraic Necessary and Sufficient Conditions for Testing Stability of 2-D Linear Systems

• 成果类型: Article
• 署名作者: Mohsenipour, Reza; Agathoklis, Panajotis
• 署名单位: University of Victoria
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2999020
• 发表日期: 2021
• 页码: 1825-1831
• 关键词: Linear systems; Stability criteria; Numerical stability; Circuit stability; asymptotic stability; testing; Continuous systems; delay; Discrete systems; mixed (hybrid) systems; STABILITY; two-dimensional (2-D) linear systems

摘要

The stability of two-dimensional (2-D) linear systems, continuous, discrete, and mixed (hybrid) cases with real or complex coefficients, is considered in this article using a single formalism. Algebraic necessary and sufficient conditions for testing the stability of these systems are developed. The conditions are based on the characteristic polynomial to be void of zero in the stability region which depends on the case being considered. These conditions consist of the stability test of few real univariate polynomials and a real generalized eigenvalue problem. The resulting stability test requires reduced computational complexity compared to existing techniques. A numerical example is given to illustrate the merits of the proposed approach.