A Linear Matrix Inequality for Robust Stability Analysis with Frequency-Dependent Multipliers

2006 ◽  
Author(s):  
M. R. Graham ◽  
M. C. de Oliveira ◽  
R. A. de Callafon
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Frequency Dependent ◽  
Robust Stability Analysis

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

scholarly journals Robust H∞ control of an uncertain bilateral teleoperation system using dilated LMIs

2021 ◽  
pp. 014233122110490
Author(s):  
Bilal Gormus ◽  
Hakan Yazici ◽  
İbrahim Beklan Küçükdemiral
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
State Feedback ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Slave System ◽  
Bilateral Teleoperation ◽  
Reference Tracking ◽  
Teleoperation System ◽  
Force Reflection

A robust state-feedback [Formula: see text] controller is proposed for an uncertain bilateral teleoperation system having norm-bounded parametric uncertainties on mass and damping coefficients of the considered master/slave system. The proposed method ensures robust stability and successful reference tracking and force reflection performance. While Lyapunov stability is used to ensures asymptotic stability, the [Formula: see text] norm from exogenous input to the controlled output is utilized in satisfying the reference tracking and force reflection. As two performance objectives and robust stability requirement are conflicting with each other, the proposed controller reduces the associated conservatism with dilated linear matrix inequalities. Standard and dilated linear matrix inequality-based robust [Formula: see text] state-feedback controllers are performed with a one degree of freedom uncertain master/slave system under reference signal and environmental-induced exogenous force. Numerical simulation results show that the dilated linear matrix inequality-based [Formula: see text] control satisfies lower [Formula: see text] norm than a standard [Formula: see text] control. Moreover, the proposed controller demonstrates a very successful performance in achieving performance objectives despite the stringent norm-bounded parameter uncertainties.

LMI-BASED ANALYSIS FOR CONTINUOUS-DISCRETE LINEAR SHIFT-INVARIANT nD SYSTEMS

2005 ◽  
Vol 14 (02) ◽  
pp. 307-332 ◽  
Author(s):  
JACEK BOCHNIAK ◽  
KRZYSZTOF GALKOWSKI
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Robust Stabilization ◽  
Multidimensional Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Stability Margins ◽  
Nd Systems

In this paper, we describe the Linear Matrix Inequality (LMI) approach to the analysis and the synthesis of continuous-discrete linear shift-invariant multidimensional systems presented in the Roesser form. We consider stability, stability margins, robust stability, stabilization and stabilization to the prescribed stability margins and robust stabilization. An example is included as illustrations of the obtained results.

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