Polytopic H∞H∞ filter design and relaxation for nonlinear systems via tensor product technique

• Polytopic H∞H∞ filter design is presented for general nonlinear systems.
• The conservatism in the polytopic representation is relaxed using TP technique.
• The relaxation algorithm has two main steps with separation property.
• The filter has smaller estimation error and more robust against disturbances.

This paper focuses on the intensive relaxation of the conservativeness inherently existing in the primitive stage of the polytopic H∞H∞ filter design for general nonlinear systems. The considered conservativeness intrinsically stems from the polytopic representation of the nonlinear system. Therefore, it is difficult to obtain a suitable polytopic representation in the case of the special requirement on small enough conservativeness. In this paper, the vertices of the polytopic representation and representation error are especially incorporated into the filter solution together, such that the deeply-relaxed filter can be achieved with the trade-off between the tightness of the vertex polytope and the representation error. Concretely, based on the TP model transformation and an ad hoc rectification, a well-adjusted polytopic representation is acquired for the nonlinear system by two independent steps, where the first step guarantees the satisfactory representation error, while the second step further assures the tightness of the vertex polytope. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the method in terms of both the polytopic filter relaxation and the filter performance.