Observer-based stabilisation of linear systems with parameter uncertainties by using enhanced LMI conditions

International audienceThis paper deals with the problem of observer-based stabilisation for linear systems with structured norm-bounded parameter uncertainties. A new design methodology is established thanks to a judicious use of some mathematical artefacts such as the well-known Young inequality and various matrix decompositions. The proposed method allows one to compute simultaneously the observer and controller gains by solving a single bilinear matrix inequality (BMI), which becomes a linear matrix inequality (LMI) by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples and evaluations of the conservatism are provided to show the effectiveness of the proposed design methodology

Convex optimization approach to observer-based stabilization of linear systems with parameter uncertainties

International audienceIn this paper we investigate the design of observer-based controller for uncertain linear systems. On the basis of the approach using the Lyapunov theory jointly with linear matrix inequalities (LMIs), and by handling judiciously the Young relation, we derive new sufficient linear matrix inequality (LMI) conditions for the asymptotic stabilizability. The proposed method allows to compute simultaneously the observer and controller gains by solving only one LMI. The developed approach is then extended to both continuous-time systems with parameter uncertainties and their Euler approximation models. We show that our approach contains, as a particular solution, the elegant results established in [1]. A numerical example is provided to compare with respect to some existing methods

Output feedback control for a class of switching discrete-time linear systems

International audienceThis paper is concerned with the output feedback control of switching linear systems without knowledge of the current switching mode. An observer-based control scheme is proposed that is based on the cascade of a Luenberger observer to estimate the continuous state, a mode estimator, and a controller fed with the estimates of both continuous state variables and mode. Conditions for the stability of such a control scheme are presented in both a noise-free setting and a noisy one because of bounded disturbances. Linear matrix inequalities are used to express such conditions with a reduced conservativeness as compared with the results available in the current literature. The effectiveness of the proposed approach is shown by means of simulations

Observer-based control design via LMIs for a class of switched discrete-time linear systems with parameter uncertainties

This paper deals with observer-based controllerdesign method via Linear Matrix Inequalities (LMIs) for a classof switched discrete-time linear systems. The main contributionconsists in providing different scenarios of the use of Finsler’sLemma to reduce the conservatism of some previous resultsin the literature. Thanks to this scenarios and the use of someother new mathematical tools, one of the objectives of this paperis to open new research directions for other control designproblems. The validity and effectiveness of the proposed designmethodologies are shown through a numerical example

Output feedback control for discrete-time linear systems by using Luenberger observers under unknown switching

International audienceThis note deals with the problem of the design of observer-based controllers for linear switching systems without having at disposal the current knowledge of the switching mode. An estimate of switching mode is obtained by using a moving-horizon estimator and used in a output feedback scheme with a Luenberger observer and a controller fed with the state estimated by such an observer. Conditions for the stability of the proposed control scheme are presented that can be expressed in terms of linear matrix inequalities. Simulation results show the effectiveness of the approach as for both estimation method and stabilization capability

New decentralized control design for interconnected nonlinear discrete-time systems with nonlinear interconnections

This paper deals with a new decentralizedobserver-based controller design method for nonlinear discretetimeinterconnected systems with nonlinear interconnections.Thanks to some algebraic transformations and the use of anew variant of Young’s inequality, an LMI-based approachis provided to compute the observer-based controller gainmatrices. Furthermore, the congruence principle is used undera judicious and new manner leading to include additional slackvariables and to cancel some bilinear matrix coupling. Theeffectiveness of proposed methodology is shown through anillustrative example

A robust decentralized observer-based stabilization method for interconnected nonlinear systems: Improved LMI conditions

This chapter presents a new decentralized observer-based controller design method for nonlinear discrete-time interconnected systems with nonlinear interconnections. Thanks to some algebraic transformations and the use of a new variant of Young’s inequality, an linear matrix inequality (LMI)-based approach is provided to compute the observer-based controller gain matrices. Furthermore, the congruence principle is used under a judicious and new manner to include additional slack variables and to cancel some bilinear matrix coupling. The resulting final LMI conditions are less conservative compared with the techniques existing in the literature. The effectiveness of the proposed methodology is shown through two illustrative examples