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.
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 required is both the matrices A and B as seen in the form above.
The Optimization ProblemEdit
The goal of the optimization is to find a valid symmetric P such that the following LMI is satisfied.
The LMI: LMI for Schur stabilizabilityEdit
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:
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.
A link to Matlab codes for this problem in the Github repository:
 - Schur Stabilization
 - LMI in Control Systems Analysis, Design and Applications
Return to Main PageEdit
 -Matrix and LMI Properties and Tools