Controllability and observability of linear time-varying impulsive systems

Many practical systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. These complex dynamical behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability issues for a general time-varying impulsive control systems. Sufficient and necessary conditions for state controllability and state observability of the impulsive control systems are established and their applications to time-invariant impulsive control systems are also discussed. Furthermore, several new results associated with variation of parameters for time-varying impulsive control systems are derived.