Impulse Controllability for Singular Hybrid Coupled Systems

This study examines the concept of impulse controllability within singular hybrid coupled systems through the utilisation of decentralised proportional plus derivative (P-D) output feedback. By employing the Differential Mean Value Theorem, the nonlinear model can be converted into a linear parameter-varying large-scale system. Our analysis leads to the establishment of algebraic conditions that are both necessary and sufficient for the existence of a decentralised P-D output feedback controller that can guarantee impulse controllability in these complex systems. Moreover, we address the issue of admissibility within these systems by employing matrix trace inequalities. We present a novel sufficient condition for impulse controllability, which offers a new perspective on addressing this challenging problem. To validate our findings, we present numerical examples that demonstrate the effectiveness of the proposed methodologies in practice.