A new type of impulsive observer for hyperchaotic system

Abstract

This paper proposes a new observer scheme for chaotic and hyperchaotic systems. Firstly, a classical impulsive observer is investigated for Lorenz chaotic system. This approach is based on sufficient conditions for stability of impulsive dynamical systems. After, an hybrid observer is proposed for hypoerchaotic systems. Simulation results highlight the well founded of such observer design and show that the discrete measurement may be eventually sparse.

Strange attractor identification and state observation under sparse measurements

“…In this section we first recall some stability definitions, for more details see [6], [13]. Let us consider the following dynamic:…”

“…An answer to the question iv) is proposed in [13] and will be use here for illustrated the answer to question ii). More precisely, an impulsive observer, which bypass the optimization algorithm under specific conditions, will be presented in the present paper for the first time in nonlinear context and coupled to a proposed identification algorithm.…”

“…The paper is organized as follow: in the next section some stability results for a class of impulsive systems are recalled, in section three some new impulsive observers are recalled [13], in section four a multi impulsive observers design is presented on the basis of classical multi observer design [1]. Finally, we use the proposed method on the strange attractor identification and we give an example with simulation in order to highlight the well founded of our approach and the paper and with a conclusion and perspectives.…”