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International audience; This study deals with the stabilisation of discrete-time linear systems subject to static finite-level quantisation on thecontrol inputs. Two kinds of quantisers are considered: uniform and logarithmic. The modelling of the finite-level quantisation isobtained by the application of deadzone and saturation maps to an infinite-level quantiser. From this model, conditions for thesynthesis of state feedback control laws guaranteeing the convergence of the trajectories to an attractor around the originprovided that the initial state belongs to a certain admissible set are proposed. These conditions can thus be incorporated inlinear matrix inequality-based optimisation schemes to compute the stabilising gain while minimising the size of the attractor.

This study addresses the control of linear systems subject to both sensor and actuator saturations and additive ℒ2-bounded disturbances. Supposing that only the output of the linear plant is measurable, the synthesis of stabilising output feedback dynamic controllers, allowing to ensure the internal closed-loop stability and the finite ℒ2-gain stabilisation, is considered. In this case, it is shown that the closed-loop system presents a nested saturation term. Therefore, based on the use of some modified sector conditions and appropriate variable changes, synthesis conditions in a ‘quasi’- linear matrix inequality (LMI) form are stated in both regional (local) as well as global stability contexts. Different LMI-based optimisation problems for computing a controller in order to maximise the disturbance tolerance, the disturbance rejection or the region of stability of the closed-loop system are proposed.

The anti-windup technique which can be used to tackle the problems of stability and performance degradation for linear systems with saturated inputs is dealt with. The anti-windup techniques which can be found in the literature today have evolved from many sources and, even now, are diverse and somewhat disconnected from one another. In this survey, an overview of many recent anti-windup techniques is provided and their connections with each other are stated. The anti-windup technique is also explained within the context of its historical emergence and the likely future directions of the field are speculated. The focus is on so-called ‘modern’ anti-windup techniques which began to emerge during the end of the 20th century and which allow a priori guarantees on stability to be made. The survey attempts to provide constructive LMI conditions for the synthesis of anti-windup compensators in both global and local contexts. Finally, some interesting extensions and open problems are discussed, such as nested saturations, the presence of time delays in the state or the input, and anti-windup for non-linear systems.

This paper presents a new integral control law for a boost converter that ensures the stability of large-signal operation. The integral controller is derived in two steps by means of passivity-based control theory. First, a static law, which ensures global stability, is obtained. Secondly, a combination of the storage function of this static law and a new positive semidefinite storage function results in a new integral control law. The proposed regulator satisfies the usual transient specifications and behaves robustly for parameter uncertainty. Global stability is guaranteed even if the duty cycle saturation is taken into account. Simulation and experimental results verify the theoretical predictions.

The problem of delay-dependent stabilisation of linear continuous-time systems with time delay in the state, additive bounded disturbances and limited actuators is presented. A design procedure based on the solution of coupled matrix inequalities and the use of the S-procedure is proposed. The links and the trade-offs between tolerance to both disturbance and delay, and the size of the region inside which the stability of the closed-loop saturated system is assured, are discussed.

Nonlinear state feedback controllers are exhibited for locally stabilising linear discrete-time systems with both saturating actuators and additive disturbances when the output must track a certain time-varying reference level. The objective is to bring the steady-state error due to disturbances to zero, by using a saturated controller and a dead-zone function. The objective is two-fold: to determine both a stabilising controller and a region of the state space over which the stability of the resulting closed-loop system is ensured, when the controls are allowed to saturate.