Jacques L. Willems

A new interpretation of the Akagi-Nabae power components for nonsinusoidal three-phase situations

A different interpretation of the power decomposition proposed by H. Akagi et al. (1984) for distorted three-phase situations is given. This makes it possible to generalize the technique to single-phase systems and polyphase systems and also to include rigorously zero sequence currents and voltages. >

Brief paper: Feedback stabilizability for stochastic systems with state and control dependent noise

This paper deals with linear stochastic systems with state and control dependent noise. Conditions are derived for which there exists a state feedback control such that the closed loop system is stable in the mean square sense. Particular attention is paid to the case in which there is only state dependent noise or only control dependent noise and to cases in which the noise intensities are arbitrarily large.

The apparent power concept and the IEEE standard 1459-2000

This paper rigorously considers the concept of apparent power in unbalanced three-phase situations. The analysis shows that there are various related but different concepts that can be associated with the apparent power. In particular two approaches are covered, the one relating to the literature on the single-phase sinusoidal case, the other relating to the recent IEEE Standard 1459-2000. The underlying ideas for each concept are given; the relationship and the differences between them are thoroughly discussed.

Discretized partial differential equations: Examples of control systems defined on modules

The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.

Robust Stabilization of Uncertain Systems

In this paper we consider the systems described by \[dx = Axdt + Budt + \sum_i {\sigma _i F_i xd\beta _i } \qquad {\text{or}}\qquad \dot x = Ax + Bu + \sum_i {B_i F_i (x,t)C_i x,} \] and we will derive conditions under which there exists a feedback control law

Pole assignment for linear time-invariant systems by periodic memoryless output feedback

u = Kx

Reflections on apparent power and power factor in nonsinusoidal and polyphase situations

such that the closed loop system is stable for all

Time-varying feedback for the stabilization of fixed modes in decentralized control systems

\sigma _i

On the assignment of invariant factors by time-varying feedback strategies

or (smooth) nonlinearities

The circle criterion and quadratic Lyapunov functions for stability analysis

F_i