4.7 Article

Controllability of Nonlinear Impulsive and Switching Systems With Input Delay

Journal

IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 68, Issue 2, Pages 1184-1191

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2022.3149876

Keywords

Controllability; Switches; Delays; Switching systems; Nonlinear systems; Time-varying systems; Geometry; fixed point theorem; impulsive and switching system; input delay; nonlinear system

Ask authors/readers for more resources

In this article, the controllability of nonlinear impulsive and switching systems with input delay is investigated. Two controllability conditions are developed using the fixed point method under different nonlinear constraints. The first condition considers the Lipschitz nonlinear condition and a sufficient controllability criterion is obtained using the Banach's contraction mapping principle. The second condition imposes a linear growth condition on the nonlinearity and an alternative controllability condition is developed using the Rothe's fixed point theorem. The article shows that the system controllability can be influenced by the impulsive and switching factors, beyond the delayed part and the nonlinearity. Two numerical examples are provided to verify the theory.
In this article, the controllability is investigated for nonlinear impulsive and switching systems with input delay. Using the fixed point method, two controllability conditions are developed for such systems under different nonlinear constraints. First, the Lipschitz nonlinear condition is considered. A control mapping is constructed based on the input matrix condition, and a nonlinear operator is introduced to convert the controllability into the existence of a fixed point. A sufficient controllability criterion is obtained under the Banach's contraction mapping principle. Second, a linear growth condition is imposed on the nonlinearity. A switched control mapping is constructed using the inverse of controllability matrix, and a corresponding nonlinear operator is introduced. An alternative controllability condition is then developed by resorting to the Rothe's fixed point theorem. It is shown that the system controllability can be influenced by the impulsive and switching factors, beyond the delayed part and the nonlinearity. Two numerical examples are given to verify the theory.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available