Polytopic Observer Research Articles

Considering the attractor structure of chaotic maps for observer-based synchronization problems

The main purpose of this paper is to state some sufficient conditions for global synchronization of chaotic maps. The synchronization is viewed as a state reconstruction problem which is tackled by polytopic observers. Unlike most standard observers, polytopic observers can account for a special property of chaotic dynamics. Indeed, it is shown that many chaotic maps can be described in a so-called convexified form, involving a time-varying parameter which depends on the chaotic state vector. Such a form makes it possible to incorporate knowledge on the structure of the compact set wherein the parameter lies. This set depends implicitly on the structure of the chaotic attractor. It is proved that the conservatism of the polyquadratic stability conditions for the state reconstruction, stated in a companion paper, can be reduced when the corresponding Linear Matrix Inequalities involve the vertices of the minimal convex hull of this set. Theoretical developments along with special emphasis on computational aspects are provided and illustrated in the context of adaptive synchronization.

Robust Fault Isolation of Uncertain Linear Systems: An LMI Approach

This contribution deals with the design of fault isolation observer for linear systems in the presence of both model uncertainty and disturbances. The FDI problem is investigated with the aid of frequency domain and LMI techniques. Based on the theory of polytopic observers, an optimization problem under LMI constraints is derived, which allows one to incorporate the plant polytopic uncertainty into the optimal robust observer design. In order to increase the robustness of residual evaluation, a frequency domain residual index is introduced and adaptive fault thresholds are derived. A simulation example illustrates the proposed approach.

Polytopic Observers for Nonlinear Uncertain Systems

We consider a class of dynamical systems, with uncertain nonlinear terms considered as "unknown inputs". Under the additional assumption that the uncertainty is bounded, and when the system might be not observable, we build polytopic observers providing time-varying bounds (depending on the uncertainty bounds) on the state variables. We illustrate these results on a biological model of population dynamics.

Dynamic Function and Control for Polytopic System. 1st Report. Polytopic Observer Design by LMI Formulation.

When a system is parameter dependent and its trajectories of changeable parameters are affinely located in a convex polytope set, the state estimation of such a system cannot be precisely performed by using the existing linear observer theory. In dealing with this kind of state estimation problem, the polytopic observer is developed and the algorithm is formulated by LMIs in order to obtain the solutions of Riccati inequalities in solving the estimation gain matrix. Meanwhile, the stability of the proposed polytopic observer is proved and the convergence of the state estimation is guaranteed. The effectiveness of polytopic observer is testified by simulation comparison study.