Robust adaptive switching control for Markovian jump nonlinear systems via backstepping technique
type: Item
instance of: scholarly article
title: Robust adaptive switching control for Markovian jump nonlinear systems via backstepping technique
zbMATH Open document ID: 1251.93135
DOI: 10.1155/2012/514504
author: Jin Zhu
author: Qiang Ling
author: Wanqing Xie
author: Hongsheng Xi
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: We investigate robust adaptive switching controller design for Markovian jump nonlinear systems with unmodeled dynamics and Wiener noise. The concerned system is of strict-feedback form, and the statistics information of noise is unknown due to practical limitation. With the ordinary Input-to-State Stability (ISS) extended to jump case, a stochastic Lyapunov stability criterion is proposed. By using the backstepping technique and a stochastic small-gain theorem, a switching controller is designed such that stochastic stability is ensured. Also, system states will converge to an attractive region whose radius can be made as small as possible with appropriate control parameters chosen. A simulation example illustrates the validity of this method.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 93D25
zbMATH DE Number: 6106233
zbMATH Keywords: stochastic Lyapunov stability
zbMATH Keywords: backstepping
zbMATH Keywords: stochastic small-gain theorem
Wikidata QID: Q58906038
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/514504
OpenAlex ID: W2000809486
cites work: Stability of stochastic differential equations with Markovian switching
cites work: Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems
cites work: Delay-Dependent <formula formulatype="inline"><tex>$H_{\infty }$</tex> </formula> Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays
cites work: Stabilization of Markov jump linear systems using quantized state feedback
cites work: Finite Horizon $H_{2}/H_{\infty}$ Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise
cites work: Q4336523
cites work: Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching
cites work: Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $
cites work: Switching controller design for a class of Markovian jump nonlinear systems using stochastic small-gain theorem
cites work: An Introduction to Markov Processes
cites work: Robust stability and controllability of stochastic differential delay equations with Markovian switching.
cites work: Adaptive backstepping controller design using stochastic small-gain theorem
cites work: A robust adaptive nonlinear control design
cites work: A combined backstepping and small-gain approach to adaptive output feedback control
description: scientific article; zbMATH DE number 6106233