scholarly journals On parameter-dependent Lyapunov functions for robust stability of linear systems

2004 ◽  
Author(s):  
D. Henrion ◽  
D. Arzelier ◽  
D. Peaucelle ◽  
J.-B. Lasserre
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Lyapunov Functions ◽  
Parameter Dependent

scholarly journals Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Emerson R. P. da Silva ◽  
Edvaldo Assunção ◽  
Marcelo C. M. Teixeira ◽  
Luiz Francisco S. Buzachero
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Finsler’S Lemma ◽  
Time Linear

The motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

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