Performance optimisation of sampled-data switched affine systems with limit cycle stabilisation

This paper proposes a sampled-data switching function for continuous-time switched affine systems that ensures global asymptotic stability of a limit cycle while satisfying prescribed steady-state performance requirements. The proposed state-dependent switching strategy minimises the performance degradation induced by the sampled-data constraint and is derived using arguments based on the Hamilton-Jacobi-Bellman inequality in conjunction with dynamic programming. The formulation addresses both H2 and H∞ performance indices. A nonuniform sampling period is considered and assumed to satisfy designer-specified bounds. The design conditions are expressed in terms of differential linear matrix inequalities, which can be converted into linear matrix inequalities, resulting in a computationally tractable design procedure. An academic example and a two-phase interleaved boost converter, commonly used in automotive applications, are presented to validate the proposed approach.