Section: New Results

Observer-Based Stabilization of Uncertain Nonlinear Systems

Participants : Ali Zemouche, Rajesh Rajamani [University of Minneapolis, USA] , Yan Wang [University of Minneapolis, USA] , Fazia Bedouhne [University of Tizi-Ouzou, Algeria] , Hamza Bibi [University of Tizi-Ouzou, Algeria] , Abdel Aitouche [CRIStAL, Lille] .

• Relaxed LMI conditions for switched systems and LPV systems:

  By exploiting the Finsler's lemma in a non-standard way, we derived new LMI conditions. This technique has been applied to linear switched systems with uncertain parameters [10], [40] and LPV (Linear Parameter Varying) systems with inexact parameters [39], respectively. In each case, the Finsler's inequality is exploited in a convenient way to get additional decision variables which render the LMIs less conservative than those existing in the literature. In addition to analytical comparisons, several numerical examples have been used to show the superiority of the proposed new LMI conditions.

• From LMI relaxations to sequential LMI algorithm:

  Recently, motivated by autonomous vehicle control problem, a robust observer based estimated state feedback control design method for an uncertain dynamical system that can be represented as a LTI system connected with an IQC-type nonlinear uncertainty was developed [28]. Different from existing design methodologies in which a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions, the design of the robust observer state feedback controller is formulated in this paper as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is a NP hard problem in general. The applicability of the linearization method, such as variable change method or congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. A new sequential LMI optimization method to search for a feasible solution was established. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world estimated state feedback control design.