Invariance Principles on Signal Sets

A unified framework is proposed to study the asymptotic behavior of general systems. From the view-point of signal, Lyapunov-like conditions and output functions based methods are used to help the check of stability. Furthermore, the concept of pseudo distance function is introduced to describe the desired convergence behavior of systems. The derived criteria extend the classic LaSalle invariance principle and an integral invariance principle to more general contents. Particularly, a new result is presented for time-delay time-varying systems. An interesting example illustrates the proposed idea. These applications show that the approach of signal sets can provide extra flexibility for the study of stability theory.