Continuous analogues of the Hamburger-Nevanlinna theorem and fundamental matrix inequalities of classical problems. IV: Problems on integral representation as continuous interpolation problems; from the fundamental matrix inequality (FMI) to the asymptotic relation

1987 ◽  
pp. 97-108
Author(s):  
V. È. Katsnel′son
Keyword(s):  
Integral Representation ◽  
Fundamental Matrix ◽  
Asymptotic Relation ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Interpolation Problems ◽  
Continuous Interpolation

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

scholarly journals Observer-based fault estimation for linear systems with distributed time delay

2013 ◽  
Vol 23 (2) ◽  
pp. 169-186 ◽  
Author(s):  
Anna Filasová ◽  
Daniel Gontkovič ◽  
Dušan Krokavec
Keyword(s):  
Time Delay ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Structured Matrix ◽  
Continuous Time Systems ◽  
Distributed Time Delay ◽  
And Performance ◽  
Time Systems

The paper is engaged with the framework of designing adaptive fault estimation for linear continuous-time systems with distributed time delay. The Lyapunov-Krasovskii functional principle is enforced by imposing the integral partitioning method and a new equivalent delaydependent design condition for observer-based assessment of faults are established in terms of linear matrix inequalities. Asymptotic stability conditions are derived and regarded with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. Simulation results illustrate the design approach, and demonstrates power and performance of the actuator fault assessment.

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.

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.

H∞ Dynamic output feedback control of LPV time-delay systems via dilated linear matrix inequalities

2018 ◽  
Vol 41 (2) ◽  
pp. 552-559 ◽  
Author(s):  
Imen Nejem ◽  
Mohamed Hechmi Bouazizi ◽  
Faouzi Bouani
Keyword(s):  
Linear Matrix Inequality ◽  
Output Feedback ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Linear Parameter Varying ◽  
Dynamic Output ◽  
Dynamic Output Feedback Controller ◽  
Delay Dependent

This paper uses the linear matrix inequality dilation approach to deal with robust stability and H∞ dynamic output feedback controller synthesis for linear parameter varying delayed systems with variable delay. This approach can express the original non-convex problem in terms of convex linear matrix inequalities and consequently reduces the conservatism of linear matrix inequality synthesis without dilation. Both delay-dependent stability and H∞ performance are studied in a quadratic context. Furthermore, a Lyapunov–Krasovskii functional is used to derive a delay-dependent criterion formulated in terms of a linear matrix inequality that will be used to search for an H∞ linear parameter varying delayed dynamic output feedback controller. To achieve this aim we use an integral inequality which plays a key role in the derivation of this criterion and enables the reduction of the H∞ cost in comparison to other results.

scholarly journals Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 217 ◽  
Author(s):  
Yuhong Huo ◽  
Jia-Bao Liu
Keyword(s):  
Time Delay ◽  
Stability Condition ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Matrix Inequalities

The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.

Robust Fault Estimation Based on Adaptive Observer

2013 ◽  
Vol 791-793 ◽  
pp. 888-891
Author(s):  
Zhi Yuan ◽  
Li Na Wu ◽  
Zheng Fang Wang ◽  
Jie Liu
Keyword(s):  
Linear Matrix Inequality ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Estimation Problem ◽  
Adaptive Observer ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Lmi Technique

This paper investigates the adaptive observer-based robust fault estimation problem for linear uncertain systems with disturbances. Sufficient conditions for the existence of such a fault estimation observer are given in terms of matrix inequalities. The solution is obtained by the linear matrix inequality (LMI) technique. An example is given to demonstrate the effectiveness of the proposed approach.

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