Stabilization and DOF control of discrete-time T-S fuzzy time-delay systems

Ligang Wu; Xiaojie Su; Peng Shi

doi:10.1007/978-3-319-11316-6_3

Stabilization and DOF control of discrete-time T-S fuzzy time-delay 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, the stabilization and DOF control problems are investigated for discrete-time T-S fuzzy time-delay systems. By utilizing a novel idea of delay partitioning technique, a delay-dependent stability condition with less conservativeness is proposed at first. Then, based on the stability result, the stabilization problem via the non-PDC scheme is addressed with the gain matrix of the stabilization state feedback controller, which can be obtained by solving a set of LMIs. Furthermore, we consider the DOF control problem in case some state components are not available. By applying the scaled small gain theorem and the delay partitioning method, a sufficient condition is proposed, which guarantees that the closed-loop system is asymptotically stable and has an induced l ₂ performance. Then, the desired DOF controller can be designed by the convex linearization approach, and a solvability condition for the DOF controller is also established in terms of LMIs.

Original language	English
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer International Publishing
Pages	57-77
Number of pages	21
DOIs	https://doi.org/10.1007/978-3-319-11316-6_3
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_3

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abstract = "In this chapter, the stabilization and DOF control problems are investigated for discrete-time T-S fuzzy time-delay systems. By utilizing a novel idea of delay partitioning technique, a delay-dependent stability condition with less conservativeness is proposed at first. Then, based on the stability result, the stabilization problem via the non-PDC scheme is addressed with the gain matrix of the stabilization state feedback controller, which can be obtained by solving a set of LMIs. Furthermore, we consider the DOF control problem in case some state components are not available. By applying the scaled small gain theorem and the delay partitioning method, a sufficient condition is proposed, which guarantees that the closed-loop system is asymptotically stable and has an induced l 2 performance. Then, the desired DOF controller can be designed by the convex linearization approach, and a solvability condition for the DOF controller is also established in terms of LMIs.",

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AB - In this chapter, the stabilization and DOF control problems are investigated for discrete-time T-S fuzzy time-delay systems. By utilizing a novel idea of delay partitioning technique, a delay-dependent stability condition with less conservativeness is proposed at first. Then, based on the stability result, the stabilization problem via the non-PDC scheme is addressed with the gain matrix of the stabilization state feedback controller, which can be obtained by solving a set of LMIs. Furthermore, we consider the DOF control problem in case some state components are not available. By applying the scaled small gain theorem and the delay partitioning method, a sufficient condition is proposed, which guarantees that the closed-loop system is asymptotically stable and has an induced l 2 performance. Then, the desired DOF controller can be designed by the convex linearization approach, and a solvability condition for the DOF controller is also established in terms of LMIs.

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Stabilization and DOF control of discrete-time T-S fuzzy time-delay systems

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