Filter design for Markovian jump repeated scalar nonlinear systems

• DOI: 10.1016/j.jfranklin.2014.04.024
• Publication Date: 2014-05-17T15:00:46Z
• Authors: Zhong Zheng; Yuechao Ma; Fanbiao Li; Ligang Wu
• Keywords: Diagonally dominant matrix; Filtering problem

Abstract This paper is concerned with the l 2 − l ∞ filtering problem for discrete-time Markovian jump repeated scalar nonlinear systems. Our attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be stochastically stable with a prescribed weighted l 2 − l ∞ performance. By employing both the mode dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique, a sufficient condition is firstly established, which guarantees the Markovian jump repeated scalar nonlinear system to be stochastically stable with an induced l 2 − l ∞ disturbance attenuation performance. The corresponding full-order filter design is cast into a convex optimization problem, which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is presented to show the effectiveness of the proposed methods.