Stochastic Incremental Input-to-State Stability of Nonlinear Switched Systems with Brownian Motions
- PDF / 881,436 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 67 Downloads / 186 Views
Stochastic Incremental Input-to-State Stability of Nonlinear Switched Systems with Brownian Motions Yuanhong Ren1
· Weiqun Wang2
· Weisong Zhou3 · Mingxuan Shen4
Received: 22 April 2020 / Revised: 11 October 2020 / Accepted: 15 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, (reverse) mode-dependent average dwell time (MDADT) method combined with multiple incremental Lyapunov functions is utilized to investigate the stochastic incremental input-to-state stability (SIISS) of stochastic switched systems. The sufficient conditions in terms of the (reverse) MDADT scheme are extracted to ensure SIISS, while it is shown that the SIISS can still be achieved even if all subsystems are not stochastically incrementally input-to-state stable. In particular, an incremental supply rate is introduced to obtain sufficient conditions to ensure SIISS for stochastic feedback interconnected switched systems. Specifically, when the stochastic switched systems are composed of some SIISS and non-SIISS subsystems, the (reverse) MDADT method is employed to establish a relationship between these two kinds of subsystems to ensure SIISS for the stochastic switched systems. Two examples are presented to demonstrate the effectiveness of the results. Keywords Nonlinear stochastic switched systems · Stochastic incremental input-to-state stability · (Reverse) mode-dependent average dwell time · Feedback interconnected switched systems
B
Weiqun Wang [email protected] Yuanhong Ren [email protected] Weisong Zhou [email protected] Mingxuan Shen [email protected]
1
College of Science, Hebei Agricultural University, Baoding 071001, China
2
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
3
Key Lab of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
4
School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
Circuits, Systems, and Signal Processing
1 Introduction Stochastic switched system (SSS) is a particular class of stochastic hybrid systems that consist of a finite family of continuous-time or discrete-time subsystems and a random switching signal determining the active subsystems at each sample time. Due to various inevitable random factors in the running process of real systems, they should be described with the stochastic models [5,9,16,23,27,31]. Multiple subsystems and various types of switching signals in the SSS make their stability analysis difficult. Significantly, the switched signal plays a central role in system stability analysis. The average dwell time (ADT) switching characteristics have been developed for a class of typical switching signals. As the extension of dwell time (DT) switching, the ADT switching is a more flexible and efficient strategy compared with the DT switching in system stability analysis [40,41]. Furthermore, maximum DT and minimum DT have been discussed in [2] and [6], respectively. The maxi
Data Loading...
