Wim Michiels

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The instability mechanisms, related to the implementation of distributed delay controllers in the context of finite spectrum assignment, were studied in detail in the past few years. In this note we introduce a distributed delay control law that assigns a finite closed-loop spectrum and whose implementation with a sum of point-wise delays is safe. This(More)
We consider the characterization and computation of H∞ norms for a class of timedelay systems. It is well known that in the finite-dimensional case the H∞ norm of a transfer function can be computed using the connections between the corresponding singular value curves and the imaginary axis eigenvalues of a Hamiltonian matrix, leading to the established(More)
This note addresses the output feedback stabilization problem of a chain of integrators using multiple delays. We shall prove that either distinct delays or a proportional+delay compensator with 1 distinct delays are sufficient to stabilize a chain including integrators.We present two different approaches. Both are constructive and rely on frequency-domain(More)
Abstract. This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. The distributed delay, whose kernel is a gamma-distribution with a gap, represents the human drivers’ behavior in the average. The aim of the paper is to give a characterization of the regions in the(More)
An eigenvalue based approach for the stabilization of linear neutral functional differential equations is presented, which extends the recently developed continuous pole placement method for delay equations of retarded type. The approach consists of two steps. First the stability of the associated difference equation is determined and a procedure is applied(More)
We study the stability of a linear system with a pointwise, time-varying delay. We assume that the delay varies around a nominal value in a deterministic way and investigate the influence of this variation on stability. More precisely we are interested in characterizing situations where the time-varying delay system is stable, whereas the system with(More)
A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to(More)
This paper concerns the stability optimization of (parameterized) matrices A(x), a problem typically arising in the design of fixed-order or fixed-structured feedback controllers. It is well known that the minimization of the spectral abscissa function α(A) gives rise to very difficult optimization problems, since α(A) is not everywhere differentiable and(More)
This paper focuses on the static output feedback stabilization problem for a class of SISO systems when the control law includes multiple (distinct) delays. We are interested in giving necessary conditions for the existence of such stabilizing controllers. Illustrative examples (second-order system, chain of integrators, or chain of oscillators) are(More)