Stabilization of hybrid systems under state constraints

Wu, Cong; Zhao, Xudong; Xu, Ning; Han, Xiumei

doi:10.1016/j.nahs.2021.101015

Cited by 8 publications

(2 citation statements)

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“…In the study of switched systems with partial state constraints, different approaches, for example, barrier Lyapunov function method and nonlinear model predictive control, have been proposed over the last few years. For the switched systems defined on a closed hypercube as all state variables are constrained to the unit hypercube, different problems have been investigated in, for example, Su and Zhao (2012, 2014), Su and Wang (2015), Su et al (2018), Zhao and Zhao (2020), and Wu et al (2021). Based on the “min-switching” strategy, Zhao and Zhao (2020) investigated the issue of H ∞ reliable bumpless transfer control problem.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the “min-switching” strategy, Zhao and Zhao (2020) investigated the issue of H ∞ reliable bumpless transfer control problem. For the dwell-time-based method, Su and Zhao (2012, 2014), Su and Wang (2015), Su et al (2018), and Wu et al (2021) exploited the feature of the dwell-time technique: a dwell time of active subsystem can subside possible large state transients. However, it is observed that these results are required to calculate the lower bound of the (average) dwell time, which may give rise to a certain conservativeness Ma et al (2014).…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of a class of switched systems with state constraints via time-varying Lyapunov functions

Hua

Tian

2022

Transactions of the Institute of Measurement and Control

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This paper studies the stabilization problem of a class of continuous-time switched linear systems with state constraints under pre-specified dwell-time switchings. Such systems are defined on a closed hypercube as all state variables are constrained to the unit hypercube. The dwell time in this paper is an arbitrarily pre-specified rather than a calculated constant, which is independent of any parameters. First, a class of multiple time-varying Lyapunov functions is introduced to study the stability analysis, and sufficient conditions on stability of the studied switched systems without control input are derived in the framework of pre-specified dwell-time switchings. The distinguishing feature of the proposed Lyapunov functions is that this type of delicately constructed Lyapunov functions can efficiently eliminate the “jump” phenomena of adjacent Lyapunov functions at switching times. Second in the same framework of the dwell time, sufficient conditions for stabilization are proposed for that of the switched systems with state constraints by further designing state feedback controllers. Finally, two examples are provided to demonstrate the effectiveness of the proposed results. The results of this paper do not require to calculate the total time of each subsystem during which the state is saturated or non-saturated separately, which makes the pre-specified dwell-time switchings easy to apply.

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