Nonfragile $l_{2}$ –$l_{\infty}$ Fault Estimation for Markovian Jump 2-D Systems With Specified Power Bounds

Abstract

This paper addresses the nonfragile sensor fault estimation problem for a class of two-dimensional (2-D) nonlinear systems. The underlying system is described by the well-known Fornasini–Marchesini model. The system parameters are subject to abrupt changes regulated by the Markovian process for which the entries of the mode transition probability matrix are partially accessible. A novel 2-D nonfragile state estimator is constructed to achieve the sensor fault estimation where the estimator gains are allowed to be randomly perturbed. Then, together with the Lyapunov stability theory, the stochastic analysis techniques are employed to derive the sufficient conditions that guarantee the following three performance requirements: 1) the exponential stability of the estimation error dynamics; 2) the prespecified constraint on the energy-to-peak gain; and 3) the prespecified restriction on the prescribed power bound. Moreover, the estimator gains are parameterized by using the convex optimization method. Finally, a numerical example is provided to illustrate the effectiveness of the addressed estimation algorithm.