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Graph Cuts—Combinatorial Optimization in Vision
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
Note that the normal form is not unique. Beginning with any energy, we can reparametrize it into the normal form with the following algorithm: While there is any combination of (p,q)∈N and x ∈ {0, 1} that does not satisfy the second condition, repeatedly redefine hpq(0,x)←hpq(0,x)−δ,hpq(1,x)←hpq(1,x)−δ,gq(x)←gq(x)+δ,where δ = min{hpq(0, x), hpq(1, x)}.For each p∈P, redefine gp(0)←gp(0)−δ,gp(1)←gp(1)−δ,
Differentiator application in altitude control for an indoor blimp robot
Published in International Journal of Control, 2018
Yue Wang, Gang Zheng, Denis Efimov, Wilfrid Perruquetti
Consider a single-input–single-output nonlinear system, having a uniform relative degree equal to the dimension of the state vector (Dabroom & Khalil, 1997), then it can be transformed into normal form (Isidori, 2013): where (A, B, C) are canonical form matrices, and are Lipschitz continuous functions. Let be a bounded known input, then the observer equations take the following form: where a0(x) and b0(x) are nominal models of nonlinear functions a(x) and b(x), and H is the observer gain. It is shown in Esfandiari and Khalil (1992) that when the observer gain is chosen as then, the state reconstruction is achieved, where ε is a small positive parameter, and the positive constants αi are chosen to make the roots of having negative real parts (see Dabroom & Khalil, 1999). The choice of H sets the eigenvalues of (A − HC) at 1/ε times the roots of (16). According to Esfandiari and Khalil (1992), the estimation error will decay to O(ε) after a short transient period.
Unknown input observer design for linear time-invariant multivariable systems based on a new observer normal form
Published in International Journal of Systems Science, 2022
Helmut Niederwieser, Markus Tranninger, Richard Seeber, Markus Reichhartinger
Note that the proposed observer normal form consists of p coupled single-output systems of orders . In the case p = 1 the proposed observer normal form (11a) coincides with the well-known transposed observable canonical form for linear single-output systems.
Geometry of symplectic partially hyperbolic automorphisms on 4-torus
Published in Dynamical Systems, 2020
In view of this theorem, we shall call decomposable the case, when the closure of the unstable leaf of is a two-dimensional torus. Recall the theorem on the rational canonical form [17] (Frobenius normal form).