Abstract:
In this issue of Critical Care, Seely and Macklem [1] present a clear and concise overview of several methodologies used to characterize variability. Why is this report important? First, not only does it provide an opportunity to appreciate the principles of the analytical techniques, but it also gives clues for interpreting the results. Those who are unfamiliar with this field of investigation, as well as those who participated in the early time domain and spectral analysis studies but who were somewhat overwhelmed by the complexity of the more recent and elaborate multifractal and entropy analyses, will appreciate this broad overview. Second, the relevance and respective contribution of the various techniques are clearly highlighted. This is an important aspect of the overview because such information is scarce in the medical literature.Most people would be more interested in the height of the coastal waves that challenge their homes in bad weather than in the average sea level. However, as with many other elaborate research techniques, the practitioner may question the clinical relevance of cardiovascular variability, and why should he or she care about it? The clinical relevance may be even more questionable when one takes into consideration that all of these techniques do require some time and effort. No direct, online, fully automated and sophisticated variability parameters are yet available for application in the critically ill. The investigator must always verify the data before computing the variability estimates. Nonstationarities in the signals confound the time and frequency domain analyses. This also applies to power law and entropy techniques.Artifacts, ectopy, or more sustained arrhythmias will markedly affect calculations and must be carefully detected and corrected for. Many of these events are unpredictable, whereas others, such as those induced by various nursing procedures, physiotherapy and catheter flushing, must be postponed during data acqui

Abstract:
The paper shows how to compute a diffeomorphic state space transformation in order to put the initial mutivariable nonlinear model into an appropriate regular form. This form is an extension of the one proposed by Lukyanov and Utkin [9], and constitutes a guidance for a “natural” choice of the sliding surface. Then stabilization is achieved via a sliding mode strategy. In order to overcome the chattering phenomenon, a new nonlinear gain is introduced.

Abstract:
The results concern the fundamental problem of Lyapunov analysis of sliding motions. It consist first to estimate the useful part of the sliding surface (the so-called “sliding domain”) and second to estimate the useful part of the state domain that is the domain of all initial conditions for which the corresponding solutions converge to the sliding domain. The application of such results concern the design of a realistic bounded control. Several examples are exposed in order to illustrate the obtained results.

Abstract:
This paper is concerned with the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given non-symmetrical polyhedral set to be positively invariant are obtained. Then existence conditions of linear state feedback control law respecting the constraints are established, and a procedure is given in order to calculate such a controller. The paper concerns memoryless controlled systems but the results can be applied to cases of delayed controlled systems. An example is given.

Abstract:
The paper shows how to compute a diffeomorphic state space transformation in order to put the initial mutivariable nonlinear model into an appropriate regular form . This form is an extension of the one proposed by Lukyanov and Utkin [9], and constitutes a guidance for a “natural” choice of the sliding surface. Then stabilization is achieved via a sliding mode strategy. In order to overcome the chattering phenomenon, a new nonlinear gain is introduced.

Abstract:
Proportional navigation is one of the most popular and one of the most used of the guidance laws. But the way it is studied is always the same: the acceleration needed to reach a known target is derived or analyzed. This way of studying guidance laws is called “the direct problem” by the authors. On the contrary, the problem considered here is to find, from the knowledge of a part of the trajectory of a maneuvering object, the target of this object. The authors call this way of studying guidance laws “the inverse problem”.

Abstract:
A fuzzy controller with singleton defuzzification can be considered as the association of a regionwise constant term and of a regionwise non linear term, the latter being bounded by a linear controller. Based on the regionwise structure of fuzzy controller, the state space is partitioned into a series of disjoint sets. The fuzzy controller parameters are tuned in order to ensure that the ith set is included into the domain of attraction of the preceding sets of the series. If the first set of the series is included into the region of attraction of the equilibrium point, the overall fuzzy controlled system is stable. The attractors are estimated with the help of the comparison principle, using Vector Norms, which ensures the robustness with respect to uncertainties and perturbations of the open loop system.