LMIs in Control/Matrix and LMI Properties and Tools/Schur Stabilizability

LMI for Schur Stabilizability Schur Stabilization is one method of ensuring that a controller can be made to stabilize a system. The following LMI is one that determines whether or not a system is indeed Schur Stabilizable, or having the property of being able to be Schur Stabilized. The System We consider the following system: or the matrix pair (A,B). In both cases, the matrices , , , and are the state matrix, input matrix, state vector, and the input vector, respectively. The Data The data required is both the matrices A and B as seen in the form above. The Optimization Problem The goal of the optimization is to find a valid symmetric P such that the following LMI is satisfied. The LMI: LMI for Schur stabilizability The LMI problem is to find a symmetric matrix P and a matrix W satisfying: Another LMI with the same result of finding Schur Stabilizability is to find a symmetric matrix P such that: Conclusion: If the one of the above LMIs is found to be feasible, then the system is Schur Stabilizable and the Schur Stabilization LMI will always give a feasible result as well, in addition to a controller K that will Schur Stabilize the system. Implementation A link to Matlab codes for this problem in the Github repository: https://github.com/maxwellpeterson99/MAE509Code Related LMIs - Schur Stabilization External Links - LMI in Control Systems Analysis, Design and Applications Return to Main Page -Matrix and LMI Properties and Tools