Robust H∞ Output Feedback Control Design for Takagi-Sugeno Systems with Markovian Jumps: A Linear Matrix Inequality Approach

2006 ◽  
Vol 128 (3) ◽  
pp. 617-625 ◽  
Author(s):  
Sing Kiong Nguang ◽  
Peng Shi
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequality ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Control Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Takagi Sugeno

This paper investigates the H∞ output feedback control design for a class of uncertain nonlinear systems with Markovian jumps which can be described by Takagi-Sugeno models. Based on a linear matrix inequality (LMI), LMI-based sufficient conditions for the existence of a robust output feedback controller, such that the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value, are derived. An illustrative example is used to demonstrate the effectiveness of the proposed design techniques.

scholarly journals Characterization of the dual problem of linear matrix inequality for H-infinity output feedback control problem via facial reduction

2020 ◽  
Vol 32 (3) ◽  
pp. 361-384
Author(s):  
Hayato Waki ◽  
Noboru Sebe
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequality ◽  
Output Feedback ◽  
Dual Problem ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Facial Reduction ◽  
Strict Feasibility

Abstract This paper deals with the minimization of $$H_\infty $$ H ∞ output feedback control. This minimization can be formulated as a linear matrix inequality (LMI) problem via a result of Iwasaki and Skelton 1994. The strict feasibility of the dual problem of such an LMI problem is a valuable property to guarantee the existence of an optimal solution of the LMI problem. If this property fails, then the LMI problem may not have any optimal solutions. Even if one can compute parameters of controllers from a computed solution of the LMI problem, then the computed $$H_\infty $$ H ∞ norm may be very sensitive to a small change of parameters in the controller. In other words, the non-strict feasibility of the dual tells us that the considered design problem may be poorly formulated. We reveal that the strict feasibility of the dual is closely related to invariant zeros of the given generalized plant. The facial reduction is useful in analyzing the relationship. The facial reduction is an iterative algorithm to convert a non-strictly feasible problem into a strictly feasible one. We also show that facial reduction spends only one iteration for so-called regular $$H_\infty $$ H ∞ output feedback control. In particular, we can obtain a strictly feasible problem by using null vectors associated with some invariant zeros. This reduction is more straightforward than the direct application of facial reduction.

Linear matrix inequality-based model matching H2 output feedback control of a new leak tightness machine working based on hydrostatic pressure aging method

2017 ◽  
Vol 40 (5) ◽  
pp. 1711-1725
Author(s):  
Barış Can Yalçın ◽  
Ahmet Koyun
Keyword(s):  
Hydrostatic Pressure ◽  
Feedback Control ◽  
Linear Matrix Inequality ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Test Machine ◽  
Matrix Inequality ◽  
Model Matching ◽  
Leak Tightness

Fluid leaks owing to broken pipes can be a serious problem for any hydraulic system. The main reasons for pipe breakage are spontaneously changing hydrostatic and hydrodynamic pressure values inside the pipe or faults occurring during the pipe manufacturing process. Therefore, different kinds of leak tightness tests are required in many standards for approval of the pipes used in both academic researches and industrial applications. Hydrostatic pressure aging is the most common method among leak tightness test procedures. However, conventional test machines cannot reach above 700 bar owing to their mechanical specifications. In this study, the design of a new leak tightness test machine that can reach above 1200 bar and its Linear matrix inequality-based model matching H2 output feedback control have been achieved. The efficacy of the test machine and proposed controller have been shown with both simulation and experimental results.

scholarly journals TCSC Controller Design Based on Output Feedback Control with Linear Matrix Inequality

2000 ◽  
Vol 33 (5) ◽  
pp. 185-190
Author(s):  
Masachika Ishimaru ◽  
Goro Shirai ◽  
Satoru Niioka ◽  
Ryuichi Yokoyama
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequality ◽  
Output Feedback ◽  
Controller Design ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Matrix Inequality

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

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