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Parameterized LMIs in Control Theory
SIAM Journal on Control and Optimization, 2000The authors consider several control and optimization problems which can be transformed into parametrized linear matrix inequalities. They are as follows: quadratic programming including some nonconvex and nonconcave topics which can be converted into a Boolean programming task, Lyapunov function based stability and performance analysis for uncertain ...
Apkarian, Pierre, Tuan, Hoang Duong
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LMI RELAXATIONS FOR HOMOGENEOUS POLYNOMIAL SOLUTIONS OF PARAMETER-DEPENDENT LMIS
IFAC Proceedings Volumes, 2006Abstract This paper presents a systematic procedure to generate families of linear matrix inequality (LMI) conditions of finite dimension which provide a homogeneous polynomial solution of arbitrary degree for parameter-dependent LMIs defined in the unit simplex.
Ricardo C.L.F. Oliveira +1 more
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IFAC Proceedings Volumes, 2002
Abstract In this work, we present a Model Predictive Controller (MPC) based on Linear Matrix Inequalities (LMI's). As in the standard MPC algorithms, at each (sampling) time, a convex optimization problem is solved to compute the control law. The optimization involves constraints written as LMI's, including those normally associated to MPC problems ...
Ernesto Granado +3 more
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Abstract In this work, we present a Model Predictive Controller (MPC) based on Linear Matrix Inequalities (LMI's). As in the standard MPC algorithms, at each (sampling) time, a convex optimization problem is solved to compute the control law. The optimization involves constraints written as LMI's, including those normally associated to MPC problems ...
Ernesto Granado +3 more
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Coulomb interactions in Ga LMIS
Ultramicroscopy, 2008For low emission currents from around 1 microA Ga liquid-metal ion sources (LMIS) produce fine optically bright ion beams that are strongly limited by the Coulomb particle-particle interactions. We present computations of the energy spread, the beam virtual crossover size, and beam brightness based on direct numerical integration of the equation of ...
Tomás, Radlicka, Bohumila, Lencová
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Manufacturing Systems: LMI Approach
IEEE Transactions on Automatic Control, 2006This note deals with the control of production systems that produce many part types with limited capacity. First, a simple model is used to show that the inventory control problem can be solved using modern control theory. A state feedback controller that forces the cumulative production of the system to track precisely the cumulative demand is ...
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NONCOMMUTATIVE CONVEXITY VS LMI'S
IFAC Proceedings Volumes, 2005Abstract Most linear control problems convert directly to matrix inequalities, MIs. Many of these are badly behaved but a classical core of problems convert to linear matrix inequalities (LMIs). In many engineering systems problems convexity has all of the advantages of a LMI.
J William Helton +2 more
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Proceedings of 1994 33rd IEEE Conference on Decision and Control, 2002
This paper describes a new MATLAB-based toolbox for control design via linear matrix inequality (LMI) techniques. After a brief review of LMIs and of some of their applications to control, the toolbox contents and capabilities are presented. >
P. Gahinet +3 more
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This paper describes a new MATLAB-based toolbox for control design via linear matrix inequality (LMI) techniques. After a brief review of LMIs and of some of their applications to control, the toolbox contents and capabilities are presented. >
P. Gahinet +3 more
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2019
In this chapter, following an introduction on the fundamentals of linear matrix inequalities (LMIs), the application of LMIs to solve convex optimization problems, using numerical examples, is explained. Then, the robust optimization problems are formulated and solved via the LMI-based H∞ and mixed H2∕H∞ optimization techniques.
Mohammad Fathi, Hassan Bevrani
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In this chapter, following an introduction on the fundamentals of linear matrix inequalities (LMIs), the application of LMIs to solve convex optimization problems, using numerical examples, is explained. Then, the robust optimization problems are formulated and solved via the LMI-based H∞ and mixed H2∕H∞ optimization techniques.
Mohammad Fathi, Hassan Bevrani
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IEE Proceedings - Control Theory and Applications, 2004
A new method for determining a constant precompensator for reducing the effects of interactions in multivariable systems is presented. It is shown that linear matrix inequalities (LMIs) can be used in the design of precompensators to achieve diagonal dominance.
S.S. Chughtai, N. Munro
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A new method for determining a constant precompensator for reducing the effects of interactions in multivariable systems is presented. It is shown that linear matrix inequalities (LMIs) can be used in the design of precompensators to achieve diagonal dominance.
S.S. Chughtai, N. Munro
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