LMIs in Control/Click here to continue/Controller synthesis/Quadratic Schur Satbilization

LMI for Quadratic Schur Stabilization A discrete-time system is said to be stable if all roots of its characteristic equation lie in the open unit disk. This provides a condition for the stability of discrete-time linear systems with polytopic uncertainties and a linear time-invariant system with this property is called a Schur stable system. The System Consider discrete time system where , , at any . The system consist of uncertainties of the following form where ,, and The Data The matrices necessary for this LMI are , , and The LMI: There exists some X > 0 and Z such that The Optimization Problem The optimization problem is to find a matrix such that: According to the definition of the spectral norms of matrices, this condition becomes equivalent to: Using the Lemma 1.2 in LMI in Control Systems Analysis, Design and Applications (page 14), the aforementioned inequality can be converted into: Conclusion: The Controller gain matrix is extracted as It follows that the trajectories of the closed-loop system (A+BK) are stable for any Implementation https://github.com/JalpeshBhadra/LMI/blob/master/quadratic_schur_stabilization.m Related LMIs Schur Complement Schur Stabilization 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. LMI in Control Systems Analysis, Design and Applications