Research Projects

A switched system is a family of systems and a switching logic that controls switching between elements in the family. These systems are used in various applications, including power systems, automotive control, aircraft and air traffic control, and network and congestion control. Stability of switched systems under commutation relations among constituent subsystems is well explored in literature. If the subsystems are individually stable and commute pairwise, a common Lyapunov function can be constructed, guaranteeing stability under arbitrary switching. If the subsystems are linear, stable, and generate a nilpotent or solvable Lie algebra, a switched system generated under arbitrary switching is stable. However, the relationship between the properties of Lie algebra generated by the constituent subsystems and the stability of switched systems is not explored beyond preliminary studies. To address this issue, Agrachev et al. characterized stability of switched linear systems under arbitrary switching in terms of "closeness" to nice Lie algebraic properties. This project aims to derive new conditions for robust stability of switched nonlinear systems based on properties of Lie algebra generated by the constituent subsystems.