Lyapunov Function and Exponential Trichotomy on Time Scales

Lyapunov Function and Exponential Trichotomy on Time Scales

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Exponential Stability of Linear Time-Invariant Systems on Time Scales

Several notions of exponential stability of linear time-invariant systems on arbitrary time scales are discussed. We establish a necessary and sufficient condition for the existence of uniform exponential stability. Moreover, we characterize the uniform exponential stability of a system by the spectrum of its matrix. In general, exponential stability of a system can not be characterized by the ...

Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales

with A. being a given m × m-matrix function, has been an intensively discussed field in both theory and practice. This problem can be seen in many real problems, such as in electric circuits, chemical reactions, and vehicle systems. März in 1 has dealt with the question whether the zero-solution of 1.1 is asymptotically stable in the Lyapunov sense with f t, x′ t , x t Bx t g t, x′ t , x t , wi...

Fuzzy Lyapunov stability and exponential stability in control ‎systems‎

Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...