Stability and stabilizability of linear time-invariant interval systems

• Published in: ISA transactions Vol. 145; pp. 273 - 284
• Main Authors: Wang, Zhuo, Xu, Tiexiao
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.02.2024
• Subjects: Feedback stabilization design; LTI interval systems; Parameter vertex matrices; Stability; Stabilizability; Stabilizability; Feedback stabilization design; Parameter vertex matrices; Stability; LTI interval systems
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2023.11.027

In this paper, some new approaches for stability and stabilizability determination as well as state feedback stabilization controllers of linear time-invariant (LTI) interval systems are proposed. The presented stability conditions are less conservative than those of Kharitonov’s theorem, and Gerschgorin’s disc theorem methods. Moreover, some of the proposed stability, stabilizability, and feedback stabilization control methods for LTI interval systems are proved to be sufficient and necessary conditions. Compared with some traditional stability analysis and feedback stabilization design methods for LTI interval systems, these new approaches have lower computational complexity because of a special form of parameter vertex matrices developed in this work. Some numerical and practical examples are given to demonstrate the effectiveness and advantages of the proposed methods. •The proposed stability conditions are less conservative compared to traditional methods.•One of the state feedback stabilization control methods is proven to be both a sufficient and necessary condition.•The computational complexity of the proposed strategies is substantially reduced, courtesy of the KCV matrix.