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Multi-objective Control for T-S Fuzzy Singularly Perturbed Systems

  • Chunyu Yang
  • Qingling Zhang
  • Linna Zhou
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 435)

Abstract

In this chapter, we consider the problem of multi-objective control for T-S fuzzy singularly perturbed systems. The problem consists of H  ∞  control, pole placement and singular perturbation bound design. Specifically, given an H  ∞  performance bound γ > 0, an LMI stability region \(\textbf D\) and an upper bound ε 0 for the singular perturbation parameter ε, we will construct an ε-dependent state feedback controller, such that ∀ ε ∈ (0, ε 0], the L 2-gain of the mapping from the exogenous input noise to the regulated output is less than or equal to γ and the poles of each subsystem are all within the LMI stability region \(\textbf D\). Two sub-problems of the multi-objective control are discussed and the main problem is then solved. An ε-dependent state feedback controller is designed by solving a set of ε-independent LMIs. It is shown that the controller is well-defined ∀ ε ∈ (0, ε 0]. If ε 0 is sufficiently small, the controller can be reduced to an ε-independent one. At last, an inverted pendulum controlled by a dc motor via a gear train is used to illustrate the obtained approach.

Keywords

Singular Perturbation Inverted Pendulum State Feedback Controller Pole Placement Gear Train 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Information and Electrical EngineeringChina University of Mining and TechnologyXuzhouP.R. China
  2. 2.College of SciencesNortheastern UniversityShenyangChina, People’s Republic

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