LMIs in Control/Stability Analysis/LMI for Schur Stabilization

The System We consider the following system: where , are the state vector and the input vector, respectively. Moreover, the state feedback control law is defined as follows: Thus, the closed-loop system is given by: The Data The Optimization Problem Find a matrix such that, According to the definition of the spectral norms of matrices, this condition becomes equivalent to: One can use the Lemma 1.2 in [1] page 14, the aforementioned inequality can be converted into: The LMI: LMI for Schur stabilization Title and mathematical description of the LMI formulation. Conclusion: This problem is a special case of Intensive Disk Region Design (page 230 in [1]). This problem may not have a solution even when the system is stabilizable. In other words, once there exists a solution, the solution is robust in the sense that when there are parameter perturbations, the closed-loop system's eigenvalues are not easy to go outside of a circle region within the unit circle [1]. Implementation A link to Matlab codes for this problem in the Github repository: https://github.com/asalimil/LMI-for-Schur-Stability Related LMIs LMI for Hurwitz stability External Links A list of references documenting and validating the LMI. - LMI in Control Systems Analysis, Design and Applications Return to Main Page: