Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities

Automatica ◽

10.1016/j.automatica.2003.07.001 ◽

2003 ◽

Vol 39 (12) ◽

pp. 2149-2156 ◽

Cited By ~ 17

Author(s):

Yasuaki Oishi ◽

Hidenori Kimura

Keyword(s):

Computational Complexity ◽

Linear Matrix Inequalities ◽

Randomized Algorithms ◽

Linear Matrix ◽

Matrix Inequalities ◽

Parameter Dependent

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Randomized algorithms to solve parameter-dependent linear matrix inequalities and their computational complexity

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) ◽

10.1109/cdc.2001.981208 ◽

2003 ◽

Cited By ~ 18

Author(s):

Y. Oishi ◽

H. Kimura

Keyword(s):

Computational Complexity ◽

Linear Matrix Inequalities ◽

Randomized Algorithms ◽

Linear Matrix ◽

Matrix Inequalities ◽

Parameter Dependent

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Polynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities

Automatica ◽

10.1016/j.automatica.2006.09.020 ◽

2007 ◽

Vol 43 (3) ◽

pp. 538-545 ◽

Cited By ~ 49

Author(s):

Yasuaki Oishi

Keyword(s):

Linear Matrix Inequalities ◽

Polynomial Time ◽

Linear Matrix ◽

Matrix Inequalities ◽

Polynomial Time Algorithms ◽

Parameter Dependent

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Implementation of a randomized algorithm for solving parameter-dependent linear matrix inequalities

Proceedings of the 2004 IEEE International Conference on Control Applications, 2004. ◽

10.1109/cca.2004.1387533 ◽

2005 ◽

Cited By ~ 2

Author(s):

Y. Oishi

Keyword(s):

Linear Matrix Inequalities ◽

Randomized Algorithm ◽

Linear Matrix ◽

Matrix Inequalities ◽

Parameter Dependent

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A successive constraint approach to solving parameter-dependent linear matrix inequalities

Comptes Rendus Mathematique ◽

10.1016/j.crma.2017.05.001 ◽

2017 ◽

Vol 355 (6) ◽

pp. 723-728

Author(s):

Robert O'Connor

Keyword(s):

Linear Matrix Inequalities ◽

Linear Matrix ◽

Matrix Inequalities ◽

Parameter Dependent ◽

Constraint Approach

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Existence of Homogeneous Polynomial Solutions for Parameter-Dependent Linear Matrix Inequalities with Parameters in the Simplex

Proceedings of the 45th IEEE Conference on Decision and Control ◽

10.1109/cdc.2006.377429 ◽

2006 ◽

Cited By ~ 42

Author(s):

P.-A. Bliman ◽

R. C. L. F. Oliveira ◽

V. F. Montagner ◽

P. L. D. Peres

Keyword(s):

Linear Matrix Inequalities ◽

Homogeneous Polynomial ◽

Linear Matrix ◽

Matrix Inequalities ◽

Polynomial Solutions ◽

Parameter Dependent

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Gain Scheduling Controller Synthesis with Spline-Type Parameter-Dependent Quadratic Forms via Dilated Linear Matrix Inequalities

Proceedings of the 44th IEEE Conference on Decision and Control ◽

10.1109/cdc.2005.1582340 ◽

2006 ◽

Cited By ~ 5

Author(s):

Y. Hamada ◽

I. Yamaguchi ◽

T. Kida

Keyword(s):

Linear Matrix Inequalities ◽

Quadratic Forms ◽

Gain Scheduling ◽

Controller Synthesis ◽

Linear Matrix ◽

Matrix Inequalities ◽

Parameter Dependent ◽

Type Parameter

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A randomized algorithm for solving parameter-dependent linear matrix inequalities: computational experience

Proceedings of the 41st SICE Annual Conference. SICE 2002. ◽

10.1109/sice.2002.1195822 ◽

2003 ◽

Author(s):

Y. Oishi

Keyword(s):

Linear Matrix Inequalities ◽

Randomized Algorithm ◽

Computational Experience ◽

Linear Matrix ◽

Matrix Inequalities ◽

Parameter Dependent

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Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

Elektrichestvo ◽

10.24160/0013-5380-2018-10-4-19 ◽

2018 ◽

Vol 10 (10) ◽

pp. 4-19

Author(s):

Magomed G. GADZHIYEV ◽

◽

Misrikhan Sh. MISRIKHANOV ◽

Vladimir N. RYABCHENKO ◽

◽

...

Keyword(s):

Power System ◽

Electric Power ◽

Linear Matrix Inequalities ◽

Electric Power System ◽

Linear Matrix ◽

Matrix Inequalities ◽

Power System Controllers

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Gust Alleviation Based on Magnetorheological Dampers and Linear Matrix Inequalities

10.26678/abcm.cobem2019.cob2019-1525 ◽

2019 ◽

Author(s):

Pedro Stangarlin ◽

Frederico Ribeiro ◽

Douglas Bueno

Keyword(s):

Linear Matrix Inequalities ◽

Linear Matrix ◽

Matrix Inequalities ◽

Magnetorheological Dampers ◽

Gust Alleviation

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

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331221992729 ◽

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.

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