Quasi-linear modeling and control of DC-DC converters

Hybrid dynamic modeling and control of switched affine systems: Application to DC-DC converters

“…Proof of Theorem 2. To prove the optimality property in (14), consider any solution ξ = (x, u) to H. Then for each (t, j) ∈ dom x and denoting t = t j+1 to simplify notation, we have from (18) V (x(t, j)) − V (x(0, 0))…”

“…Remark 3: It should be emphasized that once matrices P and Q i ∈ R n×n , i ∈ K have been fixed compliantly with requirement (13), the guaranteed performance level for our scheme (in terms of size of the upper bound for index J in (12) along solutions) is proportional to the inverse of η ∈ (0, 1) (see (14)). To this end, large values of η (as close as possible to 1) are expected to lead to improved LQ performance along solutions.…”

“…In other words, one may play with parameter η to suitably adjust the switching frequency along solutions. This operation clearly affects the level of guaranteed optimality, according to (14).…”

“…The problem addressed next is the computation of parameters P , Q i , i ∈ K, following some kind of optimization with the goal of reducing as much as possible the right hand side in bound (14). To this end, we make the following natural selection of matrices Q i , i ∈ K:…”

“…de Toulouse, INSA, LAAS, F-31400 Toulouse France garcia@laas.fr L. Zaccarian is with CNRS, LAAS, 7 avenue du colonel Roche, F-31400 Toulouse, Univ. de Toulouse, LAAS, F-31400 Toulouse, France and Dipartimento di Ingegneria Industriale, University of Trento, Italy zaccaian@laas.fr derive averaged models, in general bilinear, allowing the use of all the methods developed in the context of nonlinear systems (feedback linearization, flatness, passivity... see for example [12] and references therein) or, in the case of linear models obtained from linearization of bilinear averaged ones, the use of powerful linear control design techniques (see for example, [2], [9], [14]). Among the main limitations, we can point out a difficulty for quantifying the precision of the approximation obtained by averaging procedure and the fact that the control laws properties are only valid locally.…”