The Salamon-Weiss class of well-posed infinite-dimensional linear systems: A survey. (English) Zbl 0880.93021

Curtain, Ruth F.

IMA J. Math. Control Inf. 14, No. 2, 207-223 (1997).

Linear, time-invariant infinite-dimensional systems can be represented in many ways. One representation uses the maps between input, state, and output trajectories. This is the heart of what the author baptized “the Salamon-Weiss class”. Basically this class contains all systems for which any square integrable input gives a continuous state trajectory and a square integrable output trajectory, and it was introduced by Salamon and Weiss, see D. Salamon [Control and Observation of Neutral Systems (1984; Zbl 0546.93041)] and G. Weiss [SIAM J. Control Optimization 27, No. 3, 527-545 (1989; Zbl 0685.93043)]. In this paper, an overview is given of all interesting results for this class of systems. These include results on (exact) controllability, observability, stabilizability, detectability, well-posedness of feedbacks, and the linear quadratic optimal control problem. Further the paper has an extensive list of references containing (nearly) every paper written on the Salamon-Weiss class.

Reviewer: H.Zwart (Enschede)

MSC:

93C25	Control/observation systems in abstract spaces
93-02	Research exposition (monographs, survey articles) pertaining to systems and control theory
93B05	Controllability
93D15	Stabilization of systems by feedback

Keywords:

infinite-dimensional systems; Salamon-Weiss class; controllability; stabilizability; well-posedness

Citations:

Zbl 0546.93041; Zbl 0685.93043