In this paper we show how the newly introduced concept of superstable systems can be used to efficiently solve some traditionally hard design problems in control theory, such as stabilization with fixed–order controllers, rejection of bounded disturbances and robust controller design. Moreover, this approach also allows for formulating and treating some new problems such as the “linear-linear r...

We consider two-dimensional marked point processes which are Gibbsian with a two-body-potential of the form U = JV +K, where J and K depend on the positions and V depends on the marks of the two particles considered. V is supposed to have a continuous symmetry. We will generalise the famous Mermin-Wagner-Dobrushin-Shlosman theorem to this setting in order to show that the Gibbsian process is in...

Chmieliński has proved in the paper [4] the superstability of the generalized orthogonality equation |〈 f (x), f (y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmieliński by proving a theorem: Let Dn be a suitable subset of Rn. If a function f : Dn → Rn satisfies the inequality ||〈 f (x), f (y)〉|− |〈x,y〉|| ≤ φ(x,y) for an appropriate control function φ(x,y) and for all x,y ∈ Dn, ...

In this paper, we study the Baker’s superstability for the following functional equation (E (K)) ∑ φ∈Φ ∫ K f(xkφ(y)k)dωK(k) = |Φ|f(x)f(y), x, y ∈ G where G is a locally compact group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f is a continuous complex-valued function on G satisfying the Kannappan type condition, f...