The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities

2012 ◽  
Vol 192 ◽  
pp. 406-411
Author(s):  
Hui Zhang
Keyword(s):  
Problem Solving ◽  
Linear Algebra ◽  
Linear Matrix Inequalities ◽  
Polynomial Matrix ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Application System ◽  
And Control ◽  
Problem Data

Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

Linear Matrix Inequalities in System and Control Theory

1994 ◽  
Author(s):  
Stephen Boyd ◽  
Laurent El Ghaoui ◽  
Eric Feron ◽  
Venkataramanan Balakrishnan
Keyword(s):  
Control Theory ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
And Control

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.

Robust H∞ Control for Uncertain Nonlinear Stochastic Systems with Delayed State and Control

2011 ◽  
Vol 58-60 ◽  
pp. 685-690
Author(s):  
Cheng Wang ◽  
Yun Xu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Stochastic Systems ◽  
Stochastically Stable ◽  
Nonlinear Uncertain Systems ◽  
And Control

This paper considers the issue of robust H∞ control for a class of nonlinear uncertain systems with delayed states and control, and the feedback controller is designed. By constructing proper Lyapunov-krasovskii function, the resulting closed-loop system is stochastically stable for all admissible uncertainties, time-delays and nonlinearities, and satisfies a prescribed H∞ performance. Sufficient conditions for the system to be robustly stochastically asymptotically stable are derived, by using linear matrix inequalities and Lyapunov-krasovskii stability theory. The feedback controller is obtained by solving the linear matrix inequalities. Numerical example is provided to show the validity of the proposed approaches.

scholarly journals LMI Criteria for Admissibility and Robust Stabilization of Singular Fractional-Order Systems Possessing Poly-Topic Uncertainties

2020 ◽  
Vol 4 (4) ◽  
pp. 58
Author(s):  
Xuefeng Zhang ◽  
Jia Dong
Keyword(s):  
Fractional Order ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
And Control ◽  
Uncertain Linear Systems

The issue of robust admissibility and control for singular fractional-order systems (FOSs) with polytopic uncertainties is investigated in this paper. Firstly, a new method based on linear matrix inequalities (LMIs) is presented to solve the admissibility problems of uncertain linear systems. Then, a solid criterion of robust admissibility and a corresponding state feedback controller are derived, which overcome the conservatism of the existing results. Finally, for the sake of demonstrating the validity of proposed results, some relevant examples are provided.

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