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What is LMIs

Chapter 5
Handbook of Research on Advanced Intelligent Control Engineering and Automation
A linear matrix inequality is a convex constraint. They are a useful tool for solving a wide variety of optimization and control problems.
Published in Chapter:
On Proportional Plus Derivative State Feedback H2 Control for Descriptor Systems
Rim Zaghdoud (National School of Engineering of Tunis, Tunisia), Salah Salhi (National School of Engineering of Tunis, Tunisia), and Moufida Ksouri (National School of Engineering of Tunis, Tunisia)
Copyright: © 2015 |Pages: 27
DOI: 10.4018/978-1-4666-7248-2.ch005
Abstract
This chapter studies the control problem for linear singular systems. Firstly a proportional plus derivative feedback controller for continuous and discrete cases for descriptor systems is given, satisfying the closed loop systems normal and stable states. A necessary and sufficient condition for the solvability of this problem should be obtained in terms of linear matrix inequality. In second part, the designed controller is required to yield a cost function with guaranteed upper bound for the continuous and discrete case and also an extension for robust control is developed. Numerical examples are included to show the effectiveness of the proposed result.
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