1,055 research outputs found
The local disturbance decoupling problem with stability for nonlinear systems
In this paper the Disturbance Decoupling Problem with Stability (DDPS) for nonlinear systems is considered. The DDPS is the problem of finding a feedback such that after applying this feedback the disturbances do not influence the output anymore and x = 0 is an exponentially stable equilibrium point of the feedback system. For systems that can be decoupled by static state feedback it is possible to define (under fairly mild assumptions) a distribution Δs* which is the nonlinear analogue of the linear V*s, the largest stabilizable controlled invariant subspace in the kernel of the output mapping, and to prove that the DDPS is locally solvable if and only if the disturbance vector fields are contained in Δs*
Stable gonality is computable
Stable gonality is a multigraph parameter that measures the complexity of a
graph. It is defined using maps to trees. Those maps, in some sense, divide the
edges equally over the edges of the tree; stable gonality asks for the map with
the minimum number of edges mapped to each edge of the tree. This parameter is
related to treewidth, but unlike treewidth, it distinguishes multigraphs from
their underlying simple graphs. Stable gonality is relevant for problems in
number theory. In this paper, we show that deciding whether the stable gonality
of a given graph is at most a given integer belongs to the class NP, and we
give an algorithm that computes the stable gonality of a graph in
time.Comment: 15 pages; v2 minor changes; v3 minor change
Computing graph gonality is hard
There are several notions of gonality for graphs. The divisorial gonality
dgon(G) of a graph G is the smallest degree of a divisor of positive rank in
the sense of Baker-Norine. The stable gonality sgon(G) of a graph G is the
minimum degree of a finite harmonic morphism from a refinement of G to a tree,
as defined by Cornelissen, Kato and Kool. We show that computing dgon(G) and
sgon(G) are NP-hard by a reduction from the maximum independent set problem and
the vertex cover problem, respectively. Both constructions show that computing
gonality is moreover APX-hard.Comment: The previous version only dealt with hardness of the divisorial
gonality. The current version also shows hardness of stable gonality and
discusses the relation between the two graph parameter
Minimality of dynamic input-output decoupling for nonlinear systems
In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem
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