Filter design for Markovian jump repeated scalar nonlinear systems

This paper is concerned with the ℓ2−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 ℓ2−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 ℓ2−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.