LMIs in Control/Click here to continue/Controller synthesis/Static-State Feedback Problem

We are attempting to stabilizing The Static State-Feedback Problem The System Consider a continuous time Linear Time invariant system The Data are known matrices The Optimization Problem The Problem's main aim is to find a feedback matrix such that the system and is stable Initially we find the matrix such that is Hurwitz. The LMI: Static State Feedback Problem This problem can now be formulated into an LMI as Problem 1: From the above equation and we have to find K The problem as we can see is bilinear in The bilinear in X and K is a common paradigm Bilinear optimization is not Convex. To Convexify the problem, we use a change of variables. Problem 2: where and we find The Problem 1 is equivalent to Problem 2 Conclusion If the (A,B) are controllable, We can obtain a controller matrix that stabilizes the system. Implementation A link to the Matlab code for a simple implementation of this problem in the Github repository: https://github.com/yashgvd/ygovada Related LMIs Hurwitz Stability External Links - LMI in Control Systems Analysis, Design and Applications 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. -Mathworks reference to DC Gain Return to Main Page: