Open AccessStability analysis of 2‐D discrete and continuous state‐space systems
Author(s) -
Kanellakis Apostolos,
Tawfik Ayman,
Agathoklis Panajotis
Publication year - 2022
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12224
Subject(s) - mathematics , stability (learning theory) , state space , matrix (chemical analysis) , lyapunov equation , lyapunov function , control theory (sociology) , state (computer science) , discrete system , set (abstract data type) , computer science , algorithm , physics , statistics , control (management) , machine learning , artificial intelligence , materials science , nonlinear system , quantum mechanics , composite material , programming language
This paper presents new stability conditions for two‐dimensional (2‐D) systems in state‐space description. Both discrete and continuous systems are studied. These results are based on the criteria first presented by Huang, De Carlo, Strintzis, Murray, Delsarte, et al. and on the discrete Lyapunov equation with complex elements for 2‐D systems. The stability properties of the Mansour matrix are also used for stability testing in state‐space. Criteria for the VSHP property of 2‐D polynomials are further presented using the continuous Lyapunov equation with complex elements and the stability properties of the Schwarz matrix form. The stability properties of the Schwarz matrix are also used for testing the VSHP property of 2‐D polynomials in state‐space. The proposed new criteria are non‐conservative for the stability analysis of 2‐D discrete and continuous systems and achieve the aim of reducing the original 2‐D problem as much as possible to a set of 1‐D stability tests. Numerical examples are given to illustrate the utility of the proposed conditions.