Passive and Conservative Infinite-Dimensional Impedance and Scattering Systems (From a Personal Point of View)
نویسنده
چکیده
U is a Hilbert space. By a L(U)-valued positive analytic function on C + (= the open right half-plane) we mean an analytic function which satisfies the condition b D+ b D 0. This function need not be proper, i.e., it need not be bounded on any right half-plane. We give a complete answer to the question under what conditions such a function can be realized as the transfer function of an (impedance) passive state space system of a certain type (not necessarily well-posed). By this we mean a system which satisfies a certain energy inequality. The system is energy preserving if this energy inequality is an equality, and it is conservative if both the system and its dual are (impedance) energy preserving systems. The impulse response cannot contain a pure derivative. 5 Abstract (continues) A typical example of an impedance conservative system is a system of hyperbolic type with collocated sensors and actuators. The diagonal transform maps an impedance passive (energy preserving, conservative) system into a (wellposed) scattering passive (energy preserving, conservative) system. The Cayley transform maps a continuous time passive (energy preserving, conservative) system (impedance or scattering) into a passive (energy preserving, conservative) discrete time system. If we apply negative output feedback to an impedance passive system, then the resulting system is both wellposed and energy stable. Finally, we study lossless scattering systems, i.e., scattering conservative systems whose transfer functions are inner.
منابع مشابه
Cosmological argument in proving the existence of God from Imam Khomeini's (RA) point of view
This article reviews Cosmological argument in proving the existence of God from the viewpoint of Imam Khomeini (RA). At first, various views to the existence of God are reviewed and then its etymology will be reviewed. Cosmological argument proves God through universal premises about truth and world and and the Movement Argument, Casual Argument and Necessity and Possibility Argument are dif...
متن کاملPassive and Conservative Continuous-Time Impedance and Scattering Systems. Part I: Well-Posed Systems
متن کامل
When the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...
متن کاملNonexpansive mappings on complex C*-algebras and their fixed points
A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...
متن کاملA complete model of a finite-dimensional impedance-passive system
We extend the classes of standard discreteand continuous-time input/state/ output matrix systems by adding reverse internal and/or external channels. The reverse internal channel permits the impulse response to contain a differentiating part, and the reverse external channel allows us to include inputs which are forced to be zero and outputs which are undetermined. The purpose of this extension...
متن کامل