Stability and stabilization of discrete-time T-S fuzzy stochastic systems

Ligang Wu; Xiaojie Su; Peng Shi

doi:10.1007/978-3-319-11316-6_7

Stability and stabilization of discrete-time T-S fuzzy stochastic systems

Ligang Wu^*
, Xiaojie Su
, Peng Shi

^*Corresponding author for this work

School of Astronautics, Harbin Institute of Technology
Chongqing University
Adelaide University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In this chapter, we intend to investigate the stability and stabilization problems for discrete-time T-S fuzzy stochastic systems with time-varying delay. For a given T-S fuzzy stochastic system, our attention is focused on obtaining the sufficient conditions assuring its mean-square asymptotic stability, and designing the stabilization controller for those unstable systems. Employing the novel idea of delay-partitioning technique, we first get the parameterized LMIs by constructing basis-dependent LKF, and then transform those parameterized LMIs into strict LMIs which can be directly solved by computer software. Finally, those stability conditions are extended to settle stabilization problem via the non-PDC scheme, and the proposed theory will be applied to stabilize an inverted pendulum system.

Original language	English
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer International Publishing
Pages	157-184
Number of pages	28
DOIs	https://doi.org/10.1007/978-3-319-11316-6_7
State	Published - 2015
Externally published	Yes

Publication series

Name	Studies in Systems, Decision and Control
Volume	12
ISSN (Print)	2198-4182
ISSN (Electronic)	2198-4190

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10.1007/978-3-319-11316-6_7

Cite this

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abstract = "In this chapter, we intend to investigate the stability and stabilization problems for discrete-time T-S fuzzy stochastic systems with time-varying delay. For a given T-S fuzzy stochastic system, our attention is focused on obtaining the sufficient conditions assuring its mean-square asymptotic stability, and designing the stabilization controller for those unstable systems. Employing the novel idea of delay-partitioning technique, we first get the parameterized LMIs by constructing basis-dependent LKF, and then transform those parameterized LMIs into strict LMIs which can be directly solved by computer software. Finally, those stability conditions are extended to settle stabilization problem via the non-PDC scheme, and the proposed theory will be applied to stabilize an inverted pendulum system.",

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AU - Shi, Peng

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AB - In this chapter, we intend to investigate the stability and stabilization problems for discrete-time T-S fuzzy stochastic systems with time-varying delay. For a given T-S fuzzy stochastic system, our attention is focused on obtaining the sufficient conditions assuring its mean-square asymptotic stability, and designing the stabilization controller for those unstable systems. Employing the novel idea of delay-partitioning technique, we first get the parameterized LMIs by constructing basis-dependent LKF, and then transform those parameterized LMIs into strict LMIs which can be directly solved by computer software. Finally, those stability conditions are extended to settle stabilization problem via the non-PDC scheme, and the proposed theory will be applied to stabilize an inverted pendulum system.

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Stability and stabilization of discrete-time T-S fuzzy stochastic systems

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