Filter design for Markovian jump repeated scalar nonlinear systems

摘要

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.