Abstract. This paper considers the problem of estimating the fragility of a PI controller for a linear control system: it is required to construct admissible variation regions for the controller gains in which the closed-loop system remains stable. The method proposed below is based on the technique of linear matrix inequalities (LMIs); it reduces the original estimation problem to non-complex convex optimization problems. The non-fragility radius of a PI controller and a non-fragile bounding ellipsoid for rejecting nonrandom bounded exogenous disturbances are introduced. A simple method is described to estimate the stabilizability region as a whole. According to the numerical simulation results provided, the approach is effective. Note that this approach can be easily extended to more general problems, in particular, to the fragility analysis of PID controllers and PID controllers with an aperiodic filter.
Keywords: linear control system, PI controller, stability, fragility, non-fragility, linear matrix inequality (LMI), bounding ellipse, ellipse of admissible perturbations.
Acknowledgments. The research presented in Section 3 was supported by the Russian Science Foundation, project no. 25-29-20062, https://rscf.ru/en/project/25-29-20062/.
Mokhnacheva, A.A. and Khlebnikov, M.V., Estimating the Fragility of PI Controllers Using the Technique of Linear Matrix Inequalities and Visualization Tools. Control Sciences 2, 22–29 (2026).
Estimating the Fragility of PI Controllers Using the Technique of Linear Matrix Inequalities and Visualization Tools