Positive Definiteness in Linear Matrix Inequality Problem for $H$ -Infinity Output Feedback Control Problem

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.

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

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217690224 ◽

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.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2232686 ◽

2006 ◽

Vol 128 (3) ◽

pp. 617-625 ◽

Cited By ~ 15

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.

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

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)40958-x ◽

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

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Robust H∞ output feedback control of discrete-time switched systems via a new linear matrix inequality formulation

2010 8th World Congress on Intelligent Control and Automation ◽

10.1109/wcica.2010.5553817 ◽

2010 ◽

Author(s):

Jiao Li ◽

Yuzhong Liu ◽

Rui Mei ◽

Bo Li

Keyword(s):

Feedback Control ◽

Linear Matrix Inequality ◽

Discrete Time ◽

Output Feedback ◽

Switched Systems ◽

Output Feedback Control ◽

Linear Matrix ◽

Matrix Inequality

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Static Output-Feedback Control for Vehicle Suspensions: A Single-Step Linear Matrix Inequality Approach

Mathematical Problems in Engineering ◽

10.1155/2013/907056 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 9

Author(s):

Josep Rubió-Massegú ◽

Francisco Palacios-Quiñonero ◽

Josep M. Rossell ◽

Hamid Reza Karimi

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Output Feedback Control ◽

Vehicle Suspension ◽

Linear Matrix ◽

Static Output Feedback ◽

Matrix Inequality ◽

Feedback Controllers ◽

Feedback Information ◽

Static Output

In this paper, a new strategy to design static output-feedback controllers for a class of vehicle suspension systems is presented. A theoretical background on recent advances in output-feedback control is first provided, which makes possible an effective synthesis of static output-feedback controllers by solving a single linear matrix inequality optimization problem. Next, a simplified model of a quarter-car suspension system is proposed, taking the ride comfort, suspension stroke, road holding ability, and control effort as the main performance criteria in the vehicle suspension design. The new approach is then used to design a static output-feedbackH∞controller that only uses the suspension deflection and the sprung mass velocity as feedback information. Numerical simulations indicate that, despite the restricted feedback information, this static output-feedbackH∞controller exhibits an excellent behavior in terms of both frequency and time responses, when compared with the corresponding state-feedbackH∞controller.

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