A Lyapunov equation based mapping approach to achieve controller integrity

In this study, a new approach is proposed to determine controller parameter spaces that achieve integrity for multivariable systems. Integrity refers to the property that the closed-loop system remains stable against arbitrary failures of certain subsystems in order to increase the reliability of industrial systems. The proposed approach is based on the Lyapunov equation stability mapping technique. Instead of solving 2n equations to determine the boundaries of the stabilizing regions that is required in the standard Lyapunov approach, it is necessary and sufficient to solve at most two equations with respect to the controller parameters in the proposed approach. Using this approach, an algorithm is asserted to determine non-conservative controller gain regions that guarantee the stability of the multivariable systems when any one of the controller parameters fails to operate. Lastly, two benchmark case studies are included within the scope of this study to verify the effectiveness and correctness of the derived theoretical results.