L2-stability of hinging hyperplane models via integral quadratic constraints

This paper is concerned with L2-stability analysis of hinging hyperplane autoregressive models with exogenous inputs (HHARX). The proposed approach relies on analysis results for systems with repeated nonlinearities based on the use of integral quadratic constraints. An equivalent linear fractional representation of HHARX models is firstly derived. In this representation, an HHARX model is seen as the feedback interconnection of a linear system and a diagonal static block with repeated scalar nonlinearity. This makes it possible to exploit the aforementioned analysis results. The corresponding sufficient condition for L2-stability can be checked via a linear matrix inequality. A numerical example shows that the proposed approach is effective in practice.