Relative Controllability with Respect to Terminal State Constraint for a Class of Special Discrete-Continuous System

Abstract

In modern control theory, controllability is the most important dynamical characteristic of considered impulsive systems, therefore, the controllability problem is regarded as one of the fundamental issues of impulsive systems. The basic questions for the controllability of impulsive systems as well as for the ordinary systems without impulses and with control function are to obtain useful criteria that allow us to identify whether given dynamic systems are controllable or not. Up to now, there have been many investigation results for the controllability of different kinds of impulsive systems concerning the terminal state constraints of a point type. This paper is aimed to research relative controllability concerning the terminal state constraint of a general type in a class of linear time-varying impulsive systems. In this paper, several types of criteria for the relative controllability of such systems are established by an algebraic method, that is, especially speaking, by the matrix rank method. Some corresponding necessary and sufficient conditions for controllability in linear time-invariant impulsive systems are also obtained more compactly. Meanwhile, for given impulsive systems some equivalent relationships between many kinds of controllability are investigated and our criteria for relative controllability are compared with the existing results.