Computation of controlled invariant sets for discrete-time switched nonlinear systems with time-delay. Issue 14 (September 2021)

• Record Type: Journal Article
• Authors: Chen, Ruijuan; Li, Yinan; Liu, Jun
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 14(2021)
• Page Start: 7187
• Page End: 7202
• Publication Date: 2021-09
• Subjects: Invariant sets -- Switched nonlinear systems -- Time-delay -- Interval analysis; Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.07.004
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: We consider the concept of set invariance for discrete-time switched nonlinear systems with time-delays, referred to here as D -invariance. Specifically, the existence of controlled invariant sets for nonlinear switched systems with time-delay is proved by defining a suitable predecessor operator. As the main contribution, we use the interval analysis method to iteratively computing the inner-approximation of a controlled D -invariant set, which is a key step towards invariance control of switched nonlinear systems with time-delay. The sequence of the approximated controlled D -invariant sets are obtained by considering all possible delays within a given bounded region of the state space, so that a D -invariant set and controller that are independent of time-delay are obtained. Finally, two examples are given to show the performance of this method.