Convex Stability Analysis of Nonlinear Singular Systems via Linear Matrix Inequalities

2019 ◽  
Vol 64 (4) ◽  
pp. 1740-1745 ◽  
Author(s):  
Juan Carlos Arceo ◽  
Marcelino Sanchez ◽  
Victor Estrada-Manzo ◽  
Miguel Bernal
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Singular Systems

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

2007 ◽  
Vol 49 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Shuping Ma ◽  
Xinzhi Liu ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

scholarly journals Absolute Stability of a Class of Nonlinear Singular Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hong-Bing Zeng ◽  
Gang Chen ◽  
Shen-Ping Xiao
Keyword(s):  
Time Delay ◽  
Absolute Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Optimization ◽  
Nonlinear Singular Systems ◽  
Resulting Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the absolute stability for a class of nonlinear singular systems with time delay. By employing a new Lyapunov-Krasovskii functional with the idea of partitioning delay length, improved delay-dependent stability criteria are established. The resulting condition is formulated in terms of linear matrix inequalities (LMIs), which is easy to be verified by exiting LMI optimization algorithms. A numerical example is given to show the effectiveness of the proposed technique and its improvements over the existing results.

scholarly journals Aeroelastic stability analysis using linear matrix inequalities

2012 ◽  
Vol 34 (spe2) ◽  
pp. 545-551
Author(s):  
Douglas D. Bueno ◽  
Clayton R. Marqui ◽  
Luiz C. S. Góes ◽  
Paulo J. P. Gonçalvez
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Aeroelastic Stability

scholarly journals Robust Stability of Markovian Jumping Genetic Regulatory Networks with Mode-Dependent Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Guang He ◽  
Jian-An Fang ◽  
Xiaotai Wu
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Robust Stability ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Analysis Problem ◽  
Markovian Jumping

The robust stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks with parameter uncertainties and mode-dependent delays, which varies randomly according to the Markov state and exists in both translation and feedback regulation processes. The purpose of the addressed stability analysis problem is to establish some easily verifiable conditions under which the Markovian jumping genetic regulatory networks with parameter uncertainties and mode-dependent delays is asymptotically stable. By utilizing a new Lyapunov functional and a lemma, we derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks in the form of linear matrix inequalities. Illustrative examples are exploited to show the effectiveness of the derived linear-matrix-inequalities- (LMIS-) based stability conditions.

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