Global Conference on Mathematics and Applications (GCMA)

In this work, we study the admissibility of singular linear parameter-varying (LPV) systems by combining the Weierstrass canonical form with the C-monomial decomposition. The Weierstrass transformation is first used to rewrite the original singular system in an equivalent form, where the dynamic and algebraic components can be treated separately. This representation makes it possible to characterize the main structural properties of the system more explicitly.

To deal with the parameter dependence, the system matrices are then represented using the C-monomial decomposition. This allows the variations of the parameters to be incorporated directly into the analysis over the prescribed admissible parameter set. On this basis, sufficient conditions are obtained to guarantee the admissibility of the singular LPV system for all admissible parameter values. In particular, the conditions address the regularity, impulse-freeness, and asymptotic stability of the system.

The results provide a convenient framework for analyzing singular LPV systems with parameter-dependent matrices and can be further extended to other problems involving the stability and control of singular parameter-varying systems.