Optimal ℓ2-ℓ∞ filtering for Markovian jump repeated scalar nonlinear systems

This work studies the optimal ℓ₂-ℓ_∞ filter design problem for discrete-time Markovian jump repeated scalar nonlinear systems. The design focus is full- and reduced-order filters which guarantee the filtering error system to be stochastically stable with a prescribed weighted ℓ₂-ℓ_∞ performance. Firstly, both the mode dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique are employed to establish a sufficient condition that guarantees the Markovian jump repeated scalar nonlinear system to be stochastically stable with an induced ℓ₂-ℓ_∞ disturbance attenuation performance. Secondly, the corresponding full-order filter design is transformed into a convex optimization problem, which can be efficiently handled using standard numerical algorithms. Finally, a numerical example is presented to show the effectiveness of the proposed design.