抄録
This paper is concerned with stabilization of implicit systems via interconnection. Stability of implicit systems is defined so that every solution in the sense of Impulsive-Smooth Behavior is impulseless and convergent. Preservation of the initial values of the implicit system (initial-freedom preservation) through interconnection is adopted as a formulation of regularity of interconnection. In order to analyze stabilization with initial-freedom preservation, we define notions of complete-stabilizability and zero-detectability that generalize stabilizability and detectability of state space systems. It is shown that stabilizability via, interconnection with initial-freedom preservation is equivalent to complete-stabilizability and zero-detectability. Thus standard results on output feedback stabilization of state-space systems are extended to stabilization of implicit systems via interconnection. Further, we provide criteria for each of complete-stabilizability and zero-detectability in terms of the Kronecker form, Lyapunov equation and inequality, rank and invertibility of the system pencil.
