Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities

1997 ◽  
Vol 33 (4) ◽  
pp. 1326-1338 ◽  
Author(s):  
K.M. Grigoriadis ◽  
J.T. Watson
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Reduced Order

scholarly journals Reduced Model inH∞Vibration Control Using Linear Matrix Inequalities

2006 ◽  
Vol 13 (4-5) ◽  
pp. 469-484 ◽  
Author(s):  
Fernando Sarracini Júnior ◽  
Alberto Luiz Serpa
Keyword(s):  
Linear Matrix Inequalities ◽  
Degrees Of Freedom ◽  
External Disturbance ◽  
Reduced Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Reduced Order ◽  
Real Model ◽  
Model Reduction Technique ◽  
The Mathematical Model

Many practical problems in structural dynamics are modeled with a high number of degrees of freedom in order to properly describe the structure. A formulation to design robust controllers is theH∞technique where the controller has the same order of the mathematical model and this becomes unpractical and infeasible for most practical problems where the number of degrees of freedom is not small. One way to overcome this difficulty is to employ a model reduction technique, and design a reduced order controller based on this reduced model. In this case, it is required that the reduced controller ensures a good performance also for the nominal model (reduced) and for the real model (non-reduced) of the structure. Since the reduced controller is designed based on a truncated dynamic model, the non-modeled vibration modes can be excited causing the spillover phenomena, which is a severe undesirable effect. This work investigates the behavior of a reduced order controller obtained based on a reduced model through the Guyan reduction. TheH∞robust control and Linear Matrix Inequalities (LMI) formulations are employed to the problem of controlling a flexible structure subjected to an external disturbance. Some simulations are performed using a cantilever beam modeled by the finite element method. The results show that the Guyan reduced order model can be used to design a controller to the non-reduced model with success.

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.

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