LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Generalized H2 Norm

Generalized 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. The System Consider a continuous-time, linear, time-invariant system with state space realization where , , , amd is Hurwitz. The generalized norm of is: The Data The transfer function , and system matrices , , are known and is Hurwitz. The LMI: Generalized Norm LMIs 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: . . Conclusion: The generalized norm of is the minimum value of that satisfies the LMIs presented in this page. Implementation This implementation requires Yalmip and Sedumi. Generalized Norm - MATLAB code for Generalized Norm. Related LMIs LMI for System H_{2} Norm External Links 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. Return to Main Page: LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control