International Journal of Robust and Nonlinear Control 

Abstract: The continuous- and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H∞-suboptimal controllers, including reduced-order controllers. The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions. Thanks to such connections, the LMI-based characterization of H∞ controllers opens new perspectives for the refinement of H∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.

Abstract: This paper describes a distributed coordination scheme with local information exchange for multiple vehicle systems. We introduce second-order consensus protocols that take into account motions of the information states and their derivatives, extending first-order protocols from the literature. We also derive necessary and sufficient conditions under which consensus can be reached in the context of unidirectional information exchange topologies. This work takes into account the general case where information flow may be unidirectional due to sensors with limited fields of view or vehicles with directed, power-constrained communication links. Unlike the first-order case, we show that having a (directed) spanning tree is a necessary rather than a sufficient condition for consensus seeking with second-order dynamics. This work focuses on a formal analysis of information exchange topologies that permit second-order consensus. Given its importance to the stability of the coordinated system, an analysis of the consensus term control gains is also presented, specifically the strength of the information states relative to their derivatives. As an illustrative example, consensus protocols are applied to coordinate the movements of multiple mobile robots. Copyright © 2006 John Wiley & Sons, Ltd.

Abstract: A linear, finite-dimensional plant, with state-space parameter dependence, is controlled using a parameter-dependent controller. The parameters whose values are in a compact set, are known in real time. Their rates of variation are bounded and known in real time also. The goal of control is to stabilize the parameter-dependent closed-loop system, and provide disturbance/error attenuation as measured in induced L2 norm. Our approach uses a bounding technique based on a parameter-dependent Lyapunov function, and then solves the control synthesis problem by reformulating the existence conditions into a semi-infinite dimensional convex optimization. We propose finite dimensional approximations to get sufficient conditions for successful controller design.

Abstract: In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.

Abstract: One of the most important control problems is control under heavy uncertainty conditions. While there are a number of sophisticated methods like adaptation based on identification and observation, or absolute stability methods, the most obvious way to withstand the uncertainty is to keep some constraints by "brutal force". Indeed any strictly kept equality removes one " uncertainty dimension". The most simple way to keep a constraint is to react immediately to any deviation of the system stirring it back to the constraint by a sufficiently energetic effort. Implemented directly, the approach leads to so-called sliding modes, which become main operation modes in the variable structure systems (VSS) [55]. Having proved their high accuracy and robustness with respect to various internal and external disturbances, they also reveal their main drawback: the so-called chattering effect, i.e., dangerous high-frequency vibrations of the controlled system. Such an effect was considered as an obvious intrinsic feature of the very idea of immediate powerful reaction to the minutest deviation from the chosen constraint. Another important feature is proportionality of the maximal deviation from the constraint to the time interval between the measurements (or to the switching delay).