TY - JOUR
AU - Maherzi, Elyes
AU - Besbes, Mongi
AU - Zemmel, Sami
AU - Mhiri, Radhi
PY - 2010
TI - Synthesis of a Robust Multiobserver for the Estimation of Unknown Inputs Using the Piecewise Quadratic Functions
JF - American Journal of Applied Sciences
VL - 7
IS - 9
DO - 10.3844/ajassp.2010.1264.1276
UR - https://thescipub.com/abstract/ajassp.2010.1264.1276
AB - Problem statement: The estimation of states and the unknown inputs of a nonlinear
system described by a multimodel are done by a multiobserver. The stabilization of the
multiobserver calls upon uses both quadratic and no quadratic functions of Lyapunov. Although
the stabilization using the quadratic approach is interesting from the point of view implementation,
the step showed its limits for the multimodel. However, the problem paused by the quadratic
method lies in the obligation to satisfy several LMI with respect to the same Lyapunov matrix P,
these results are shown very conservative. Approach: To reduce the conservatism of the quadratic
approach we propose another approach which is exclusively based on Lyapunov piecewise
quadratic functions. The conditions obtained by the stabilization of the multiobserver are
expressed in term of matrix inequalities with constraints on the matrices rank. Results: The
estimation of both states and unknown inputs of a multimodel using the quadratic approach per
pieces leads to results less conservative than the quadratic approach. Academic examples illustrate
the robustness of the piecewise quadratic approach. Conclusion: In this article we proposed new
sufficient conditions of stability of a multiobserver able to the estimation of states and unknown
inputs of a nonlinear system describes by a multimodel subjected to the influence of the unknown
inputs. The study in was carried out by considering two approaches. The first approach is based on
Lyapunov quadratic functions; it is significant to note the great difficulty in finding satisfying
results by this approach for the multimodel systems. For this reason we proposed an approach
based on piecewise quadratic functions which led to interesting results (proposition 1) and less
conservative than the quadratic approach. The conditions suggested in this article concern both the
multiobserver stabilization and the estimation of states and the unknown inputs of a multimodel
with measurable variables of decision (μξ(k)). The synthesis of a multiobserver with no
measurable variables of decision is not approached. This point can constitute an interesting
prospect for this study.