Negative Imaginary Lemmas for Descriptor Systems

H∞ model reduction for negative imaginary systems

Discrete-time negative imaginary systems

In this paper we introduce the notion of a discrete-time negative imaginary system and we investigate its relations with discrete-time positive real system theory. In the framework presented here, discrete-time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function, in analogy with the case of discrete-time ...

On α- and D-negative imaginary systems

This paper is concerned with α– and D–negative imaginary systems. The definition of α–negative imaginary transfer functions is firstly introduced. Then, the relationship between negative imaginary and α–negative imaginary transfer functions is studied. By means of the generalized inverse, an α–negative imaginary lemma is proposed to test the α–negative imaginary property of transfer functions. ...

On non-proper negative imaginary systems

This paper studies non-proper negative imaginary systems. First, the concept of negative imaginary transfer functions thatmayhavepoles at the origin and infinity is introduced. Then, a generalized lemma is presented to provide a sufficient condition to characterize the non-proper negative imaginary properties of systems. The generalized lemma is given in terms of complex variable s in the quart...

Negative imaginary systems theory and applications

This presentation will cover recent developments in the theory of negative imaginary systems. The theory of negative imaginary systems arose out of a desire to provide a unified framework for the control of lightly damped structures with collocated force actuators and position sensors. The key result is a stability result which can be used design controllers guaranteed to yield robust closed lo...