LMIs in Control/Click here to continue/LMIs in system and stability Theory/Interval Quadratic Stability

An LMI to determine the quadratic stability of a system with parametric, interval uncertainties. The System Consider the system with Affine Time-Varying uncertainty where where lies in the intervals where and . The Data The matrices A and are known. The Optimization This optimization problem ensures quadratic stability of the system with k interval uncertainties using LMI constraints. lies in the hypercube. The vertices of the hypercube define the vertices of the uncertainty set is quadratically stable over if and only if there exists a P > 0 such that The LMI Conclusion Quadratic Stability Implies Stability of trajectories for any with for all Quadratic stability is conservative. Stability does not imply quadratic stability. Interval uncertainty is a special case of polytopic uncertainty. Implementation Example of implementation of the LMI https://github.com/MichaelDobos/LMI/blob/main/intervalquadraticstability.m Related LMIs Polytopic Quadratic Stability Discrete-Time Quadratic Stability External Links LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet. LMIs in Control Systems: Analysis, Design, and Applications - A textbook on LMIs in control by Duan and Yu. Return to Main Page