Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations

Many dynamic systems in physics, chemistry, biology, engineering, and infor mation science have impulsive dynamical behaviors due to abrupt jumps at ce rtain instants during the dynamical process, and these complex dynamic beha viors can be modeled by singular impulsive differential systems. This paper formulates and studies a model for singular impulsive delayed systems with uncertainty from nonlinear perturbations. Several fundamental issues such as global exponential robust stabilization of such systems are established. A simple approach to the design of a robust impulsive controller is then p resented. A numerical example is given for illustration of the theoretical results. Meanwhile, some new results and refined properties associated with the M-matrices and time-delay dynamic systems are derived and discussed.