An approach to the robust SPR problem through interpolation and avoidance: connections with the robust stability problem

Convergence of a number of adaptive recursive algorithms, with applications in identification and adaptive control, can be ensured by making a given transfer function strictly positive real (SPR). In some situations a partial knowledge of the system under study is available, thus becoming a robustness problem. In this paper we trace important connections between the classical problem of robust stability and the robust strict positive realness problem, which will allow one to design procedures for solving the robust SPR problem in several different cases