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Problem of an adaptive state observer design for nonlinear system withunknown time-varying parameters and under condition of delayed measurements isconsidered. State observation problem was raised by many researchers (see forexample Sanx et al. (2019)). In this paper the results proposed in Bobtsov etal. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al.(2022b) are developed. The problem is solved under assumption that the statematrix can be represented as sum of known and unknown parts. The output vectoris measured with a known constant delay. An adaptive observer whichreconstructs unknown state and unknown time-varying parameter is proposed.

Adaptive observer for a nonlinear system with partially unknown state matrix and delayed measurements