Focal stability of linear descriptor systems with saturating controls εneralized Riccati and Lyapunov equations approaches

The problem of local stabilization of linear continuous-time descriptor systems subject to saturating controls is addressed. The saturated closed-loop system is locally described as a polytopic model. The method of synthesis via generalized Riccati or Lyapunov equations consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the asymptotic stability and the absence of impulsive behavior for the closed-loop system are guaranteed, when control saturations effectively occur.