Piecewise Semi-Ellipsoidal Control Invariant Sets

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Computing control invariant sets is easy

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator, given by the Minkowski addition of sets, that is the basis of many of the iterative procedures for obtaining control invariant sets. Set inclusions conditions f...

Isochronous sets of invariant control systems

Ellipsoidal Sets for Static Output Feedback

The static output feedback synthesis for LTI systems is considered. It is shown to have analogies with robust analysis, in particular the existence of an output feedback gain is equivalent to the existence of some quadratic separator. These considerations lead to formulate the problem as the synthesis of an ellipsoidal set of stabilising controllers. Based on this formulation important issues a...

Homoclinic orbits in a piecewise system and their relation with invariant sets

Basic phenomena in chaos can be associated with homoclinic and heteroclinic orbits. In this paper, we present a general numerical method to demonstrate the existence of these orbits in piecewise-linear systems. We also show that the tangency of the stable and unstable manifolds, at the onset of the chaotic double-scroll attractor, changes the basin boundaries of twoα-limit sets. These changes a...