Lyapunov Equation Based Stability Mapping Approach: A MIMO Case Study

In this study, a Lyapunov Equation based stability mapping approach is proposed for MIMO systems in order to determine stability regions. Since the proposed approach is independent of the controller type and the number of the control variables, it is also applicable for SISO systems. In standard Lyapunov Equation approach, the designer should solve 2n equations to calculate the stabilizing parameter sets. However, it is necessary and sufficient to solve at most two equations in order to determine the stability boundaries in the proposed approach. Moreover, frequency sweeping that is required in most of the frequency domain based approaches is omitted in this approach since the stability problem is defined in the time domain. Several case studies are discussed within the scope of this study to verify the effectiveness of the derived theoretical results.