Reduced-order ℒ 2 –ℒ ∞ filtering for a class of nonlinear switched stochastic systems

The ℒ2–ℒ∞ filtering problem for a class of nonlinear switched stochastic systems is dealt with here. The authors attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be mean-square exponentially stable with a prescribed weighted ℒ2–ℒ∞ performance. Sufficient conditions are proposed by applying the average dwell time method and the piecewise Lyapunov function technique. The corresponding full-order filter design is cast into a convex optimisation problem, which can be efficiently handled by using standard numerical algorithms. Moreover, two sharply different approaches are proposed to solve the reduced-order filtering problem: one is the convex linearisation approach and the other is the projection approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.