Evolution semigroups and stability of time-varying systems on Banach spaces
نویسندگان
چکیده
The two main topics addressed are: (i) the relationship between internal, external, and input-output stability, and (ii) stability of time-invariant systems including a new Banach-space formula for the stability radius. With regard to (i), we show that a nonautonomous system is internally stable if and only if it is stabilizable, detectable and input-output stable; the short proof seems to be new even for finite-dimensional autonomous systems. For (ii), new formulas are given, in terms of the coefficients of the system, for the Lpnorm of the input-output operator and for the stability radius of the system.
منابع مشابه
Stability Radius and Internal Versus External Stability in Banach Spaces: An Evolution Semigroup Approach
In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include autonomous and nonautonomous systems modeled with unbounded state-space operators acting on Banach spaces. This approach allows one to apply the classical theory of strongly continuous semigroups to timevarying systems. In particul...
متن کاملConverse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces
We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.
متن کاملOn Two-parameter Dynamical Systems and Applications
In this note some useful properties of strongly continuous two-parameter semigroups of operators are studied, an exponential formula for two-parameter semigroups of operators on Banach spaces is obtained and some applied examples of two-parameter dynamical systems are discussed
متن کاملOn X ̃-frames and conjugate systems in Banach spaces
The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.
متن کاملOn Uniform Exponential Stability of Periodic Evolution Operators in Banach Spaces
The aim of this paper is to obtain some discrete-time characterizations for the uniform exponential stability of periodic evolution operators in Banach spaces. We shall also obtain a discrete-time variant for Neerven’s theorem using Banach sequence spaces and a new proof for Neerven’s theorem.
متن کامل