LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Rise Time Poles

LMI for Rise Time Poles The following LMI allows for the verification that poles of a system will fall within a rise time constraint. This can also be used to place poles for rise time when the system matrix includes a controller, such as in the form A+BK. The System We consider the following system: or the matrix , which is the state matrix. The Data The data required is the matrix A and the rise time you wish to verify. The Optimization Problem To begin, the constraint of the pole locations is as follows: , where z is a complex pole of A. We define . The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied. The LMI: LMI for Rise Time Poles The LMI problem is to find a matrix P> 0 satisfying: Conclusion: If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the rise time specification of , and the poles of A satisfy the previously defined constraint. Implementation A link to Matlab codes for this problem in the Github repository: https://github.com/maxwellpeterson99/MAE509Code Related LMIs - D-stabilization - D-stability Controller - D-stability Observer External Links - LMI in Control Systems Analysis, Design and Applications - A course on LMIs in Control by Matthew Peet Return to Main Page -Matrix and LMI Properties and Tools