Self-scheduled H-infinity control of missile via linear matrix inequalities

1995 ◽  
Vol 18 (3) ◽  
pp. 532-538 ◽  
Author(s):  
Pierre Apkarian ◽  
Jean-Marc Biannic ◽  
Pascal Gahinet
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
H Infinity ◽  
H Infinity Control

Linear Matrix Inequalities in Robust Unified Smooth Sliding Mode Controller Design

2012 ◽  
Author(s):  
Siew Min See ◽  
Johari Halim Shah Osman
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequalities ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
H Infinity ◽  
Mode Control ◽  
Mismatched Uncertainties ◽  
Guaranteed Cost ◽  
Mismatched Disturbances

Sebahagian besar masalah yang dihadapi dalam teori kawalan sistem boleh dikurangkan kepada beberapa masalah pengoptimuman cembung atau kuasi–cembung piawai yang melibatkan ketaksamaan matriks lelurus (LMI). Dengan perkembangan terbaru tentang cara titik dalaman, masalah pengoptimuman tersebut dapat diselesaikan secara efisien dengan kaedah berangka. Satu daripada aplikasi LMI boleh dilihat dalam penyelesaian masalah kawalan ragam gelincir. Sistem kawalan ragam gelincir berkemampuan supaya tidak terpengaruh secara keseluruhan oleh ketidakpastian padanan apabila berada dalam ragam gelincir. Akan tetapi, sistem masih menghadapi gangguan yang tidak diingini apabila diusik oleh ketidakpastian tidak terpadan, serta masalah gelugutan. Dalam kertas kerja ini, permukaan gelincir direka bentuk dengan integrasi suatu kriteria H infiniti terjamin kos optimum untuk mengurangkan gangguan tidak terpadan. Permukaan kos terjamin tersebut diterbitkan daripada prosedur pengoptimuman cembung yang diformulasikan sebagai masalah LMI. Satu kawalan licin seragam diaplikasikan untuk menyelesaikan masalah gelugutan. Keputusan menunjukkan bahawa pengawal tersebut dapat memperbaiki prestasi dari segi penyingkiran gelugutan secara keseluruhan dan penyisihan gangguan tidak terpadan Kata kunci: Ketaksamaan matriks lelurus (LMI), kawalan ragam gelincir, gangguan tidak terpadan, bebas gelugutan, kriteria H infiniti terjamin kos optimum A wide range of problems encountered in system control theory can be reduced to a few standard convex or quasiconvex optimisation problems involving linear matrix inequalities (LMI). With recent developed of interior point methods, the optimisation problems can be solved numerically very efficiently. One of the applications of the LMI may be seen in solving the sliding mode control problems. The sliding mode control system is capable of total invariance to the matched uncertainties while remain in the sliding mode. But the system may still face the undesirable distractions cause by the mismatched uncertainties, and chattering problem. In this paper, the sliding surface is designed with integration of an optimal guaranteed cost H infinity criterion to attenuate the mismatched disturbances. The guaranteed cost surface is derived from a convex optimisation procedure formulated as an LMI problem. A unified smooth control law is applied to solve the chattering problem. The results showed that the controller may improve the performance with total chattering elimination and mismatched disturbances rejection. Key words: Linear matrix inequalities (LMI), sliding mode control, mismatched uncertainties, chattering free, optimal guaranteed cost H infinity criterion

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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