Geometric Solvability and Stability Analysis of Discrete-Time Nonlinear Singular Systems

Modern engineering systems are increasingly complex, often exhibiting singular dynamics and switching behaviors that challenge traditional control methods. Ensuring reliable and efficient control in such settings is crucial for enabling technological innovation across domains such as robotics, energy, and process automation.

This research explores solvability and stability approaches as a foundation for advancing technology innovation in model-based control design of singular switched nonlinear systems. While such systems frequently arise in engineering applications, their inherent singularities and switching dynamics pose significant challenges for solvability analysis, stability guarantees, control design, and real-world implementation. Building on geometric solvability theory, the research aims to develop novel methods that ensure feasible control solutions under practical constraints and extend the analysis to robust stability frameworks, bridging the gap between mathematical rigor and engineering practice.