Robust controller synthesis via non-linear matrix inequalities

1999 ◽  
Vol 72 (11) ◽  
pp. 971-980 ◽  
Author(s):  
Emmanuel G. Collins ◽  
Debashis Sadhukhan ◽  
Layne T. Watson
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
Non Linear

scholarly journals Guaranteed Cost Nonfragile Robust Controller for Walking Simulation of Quadruped Search Robot on a Slope of VRML Model

2014 ◽  
Vol 6 ◽  
pp. 948795
Author(s):  
Peng Wang ◽  
Jixiang Li ◽  
Yuan Zhang
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Modeling Language ◽  
Displacement Curve ◽  
Model Structure ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
3D Terrain ◽  
Guaranteed Cost

The problem of walking simulation for the quadruped search robot on a slope is described as an uncertainty system. In order to create the virtual ramp road environment, VRML modeling language is used to build a real environment, which is a 3D terrain scene in Matlab platform. According to the VRML model structure of the quadruped search robot, a guaranteed cost nonfragile robust controller is designed for ramp road walking simulation. The constraint inequation is transformed into a strict linear inequality by using two equalities; the controller and the guaranteed cost upper bound are given based on the solutions of the linear matrix inequality. And the approaches of designing the controller are given in terms of linear matrix inequalities. The walking stability of quadruped search robot is observed using the VRML model established with the change of gravity curve. Simulation results show that the gravity displacement curve of the robot is smooth. The results given by linear matrix inequalities indicate that the proposed guaranteed cost controller is correct and effective.

scholarly journals Linear Matrix Inequalities in multivariable ship’s steering

2012 ◽  
Vol 19 (Special) ◽  
pp. 37-44 ◽  
Author(s):  
Monika Rybczak
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Pid Controllers ◽  
Linear Matrix ◽  
Programming Environment ◽  
Matrix Inequalities ◽  
Matlab Simulink ◽  
Ship Model ◽  
Ship Control

ABSTRACT This paper explains the basics of the Linear Matrix Inequalities (LMI), with examples of simulations and calculations created in Matlab/Simulink programming environment where the controlled plant is the “Blue Lady” ship model. First chapter of this paper gives a short overview of publications describing the use of Linear Matrix Inequalities method. Second chapter contains basic definitions and equations for the LMI method. Chapter three presents the use of LMI method for ship control by describing controller synthesis for the “Blue Lady”. Chapter four compares the operation of two controllers, the first one consisting of three independent proper adjusted PID controllers and the second one being a multivariable LMI controller. Finally conclusions from the above comparison are drawn.

scholarly journals Synthesis of Decentralized Variable Gain Robust Controllers with GuaranteedL2Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Shunya Nagai ◽  
Hidetoshi Oya
Keyword(s):  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Matching Condition ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
Interconnected System ◽  
Variable Gain

We consider a design problem of a decentralized variable gain robust controller with guaranteedL2gain performance for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller with guaranteedL2gain performance are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

scholarly journals Synthesis of Adaptive Robust Controllers for a Class of Nonlinear Systems with Input Saturations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Kenta Oba ◽  
Hidetoshi Oya ◽  
Tomohiro Kubo ◽  
Tsuyoshi Matsuki
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear Matrix Inequalities ◽  
Design Problem ◽  
Sufficient Conditions ◽  
Matching Condition ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controllers ◽  
Robust Controller

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

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