scholarly journals Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization

2017 ◽  
Vol 27 (2) ◽  
pp. 725-758 ◽  
Author(s):  
Ramtin Madani ◽  
Somayeh Sojoudi ◽  
Ghazal Fazelnia ◽  
Javad Lavaei
Keyword(s):  
Convex Optimization ◽  
Linear Matrix Inequalities ◽  
Low Rank ◽  
Linear Matrix ◽  
Matrix Inequalities

On the Low Rank Solutions for Linear Matrix Inequalities

2008 ◽  
Vol 33 (4) ◽  
pp. 965-975 ◽  
Author(s):  
Wenbao Ai ◽  
Yongwei Huang ◽  
Shuzhong Zhang
Keyword(s):  
Linear Matrix Inequalities ◽  
Low Rank ◽  
Linear Matrix ◽  
Matrix Inequalities

Linear Matrix Inequalities Approach to Input Covariance Constraint Control With Application to Electronic Throttle

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Ali Khudhair Al-Jiboory ◽  
Andrew White ◽  
Shupeng Zhang ◽  
Guoming Zhu ◽  
Jongeun Choi
Keyword(s):  
Convex Optimization ◽  
Control Problem ◽  
Linear Matrix Inequalities ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Base Line ◽  
Optimization Approach ◽  
Matrix Inequalities ◽  
Electronic Throttle ◽  
Comparison Results

In this paper, the input covariance constraint (ICC) control problem is solved by convex optimization subject to linear matrix inequalities (LMIs) constraints. The ICC control problem is an optimal control problem that is concerned to obtain the best output performance subject to multiple constraints on the input covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the ICC control problem. Both continuous- and discrete-time problems are considered. To validate our scheme in real-world systems, ICC control based on convex optimization approach was used to control the position of an electronic throttle plate. The controller performance compared experimentally with a well-tuned base-line proportional-integral-derivative (PID) controller. Comparison results showed that not only better performance has been achieved but also the required control energy for the ICC controller is lower than that of the base-line controller.

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

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

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 Contractors and Linear Matrix Inequalities

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Jeremy Nicola ◽  
Luc Jaulin
Keyword(s):  
Fixed Point ◽  
Large Class ◽  
Linear Matrix Inequalities ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Constraints ◽  
Linear Matrix ◽  
Nonlinear Constraints ◽  
Matrix Inequalities ◽  
Convex Constraints

Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.

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