LMIs in Control/Matrix and LMI Properties and Tools/Generalized H2 Norm
The norm characterizes the average frequency response of a system. To find the H2 norm, the system must be strictly proper, meaning the state space represented matrix must equal zero. The H2 norm is frequently used in optimal control to design a stabilizing controller which minimizes the average value of the transfer function, as much as possible. This optimal control problem is also called the Linear Quadratic Gaussian.
Consider a continuous-time, linear, time-invariant system with state space realization where , , , amd is Hurwitz. The generalized norm of is:
The transfer function , and system matrices , , are known and is Hurwitz.
The LMI: Generalized Norm LMIsEdit
The inequality holds under the following conditions:
1. There exists and where such that:
2. There exists and where such that:
3. There exists and where such that:
The generalized norm of is the minimum value of that satisfies the LMIs presented in this page.
This implementation requires Yalmip and Sedumi.
Generalized Norm - MATLAB code for Generalized Norm.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013.
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LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control