Reachable set bounding for linear systems with mixed delays and state constraints

• Published in: Applied mathematics and computation 2022-07, Vol.425, p.127085, Article 127085
• Main Authors: Chen, Ruihan, Guo, Moxuan, Zhu, Song, Qi, Yongqiang, Wang, Min, Hu, Junhao
• Format: Article
• Language: English
• Subjects: Lyapunov–Krasovskii functional; Mixed delays systems; Reachable set
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127085

•This paper considers the state constraint problem in reachable set estimation.•Instead of using the commonly used reciprocally convex combination method, this paper uses a less conservative method, which reduced the related decision variables.•Parameter-dependent L-K functional are constructed for the condition of uncertain differentiable parameters. This paper studies the reachable set estimation for systems with mixed delays and state constraints. Firstly, by constructing an appropriate maximal Lyapunov–Krasovskii functional, combined with the wirtinger-based integral inequality and the extended reciprocally convex combination method, we derive a new criterion about reachable set estimation which reduces the related decision variables without increasing the computational burden. Then, the results are extended to polytopic uncertainties systems and we consider the condition of uncertain differentiable parameters. Three examples are presented to demonstrate the validity of our theorems.