Robust observer-based stabilization of Lipschitz nonlinear uncertain systems via LMIs - Discussions and new design procedure

Ali Zemouche (1, 2) , Rajesh Rajamani (3) , Houria Kheloufi (4) , Fazia Bedouhene (4)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 ECE - Department of Electrical and Computer Engineering [Minneapolis]
4 LMPA - Laboratoire de Mathématiques Pures et Appliquées [Tizi-Ouzou]

This paper presents a new observer-based controller design method for Lipschitz nonlinear systems with uncertain parameters and math formula-bounded disturbance inputs. In the presence of uncertain parameters, the separation principle is not applicable even in the case of linear time invariant systems. A state of the art review for uncertain linear systems is first presented to describe the shortcomings and conservatism of existing results for this problem. Then a new LMI-based design technique is developed to solve the problem for both linear and Lipschitz nonlinear systems. The features of the new technique are the use of a new matrix decomposition, the allowance of additional degrees of freedom in design of the observer and controller feedback gains, the elimination of any need to use equality constraints, the allowance of uncertainty in the input matrix and the encompassing of all previous results under one framework. An extensive portfolio of numerical case studies is presented to illustrate the superiority of the developed design technique to existing results for linear systems from literature and to illustrate application to Lipschitz nonlinear systems.

Mots clés: Linear Matrix Inequalities (LMIs); Observer-based control; uncertain systems; Lipschitz nonlinear systems; H∞ control

Domaines: Automatique; Sciences de l'ingénieur [physics]

Ali Zemouche, Rajesh Rajamani, Houria Kheloufi, Fazia Bedouhene. Robust observer-based stabilization of Lipschitz nonlinear uncertain systems via LMIs - Discussions and new design procedure. International Journal of Robust and Nonlinear Control, 2017, 27 (11), pp.1915-1939. ⟨10.1002/rnc.3644⟩. ⟨hal-01567359⟩