LMIs in Control/Click here to continue/Controller synthesis/Quadratic Polytopic Full State Feedback Optimal H2 Control

Quadratic Polytopic Full State Feedback Optimal Control For a system having polytopic uncertainties, Full State Feedback is a control technique that attempts to place the system's closed-loop system poles in specified locations based on performance specifications given, such as requiring stability or bounding the overshoot of the output. By minimizing the norm of this system we are minimizing the effect noise has on the system as part of the performance specifications. The System Consider System with following state-space representation. where , , , , , , , , , , , , , for any . Add uncertainty to system matrices New state-space representation The Data The matrices necessary for this LMI are The Optimization Problem: Recall the closed-loop in state feedback is: This problem can be formulated as optimal state-feedback, where K is a controller gain matrix. The LMI: An LMI for Quadratic Polytopic Optimal State-Feedback Control Conclusion: The Optimal State-Feedback Controller is recovered by Implementation: https://github.com/JalpeshBhadra/LMI/blob/master/H2_optimal_statefeedback_controller.m Related LMIs Optimal State-Feedback Controller 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.