The bounded-real lemma for two-dimensional systems

The lossless bounded-real lemma for 2D systems is developed. This is based on the second local state-space (LSS) model of E. Fornasini and G. Marchesini (Math. Syst. Theory, vol.12, p.59-72, 1978; IEEE Trans. Circuits Syst. vol.CAS-27, p.1210-7, 1980). A condition for a 2D system to be bounded-real is also investigated. Similar arguments can be applied to the Roesser LSS model. The lossless bounded-real property is treated in conjunction with the asymptotic stability and the overflow oscillation in 2D systems