What is the minimum function observer order

The design of minimal order observer which can estimate the state feedback control signal Kx(t) with arbitrarily observer poles and K, has been tried for years, with the prevailing conclusion that it is an unsolved problem. This paper asserts for the first time, that this design problem can be simplified to a set of linear equations K=K_z diag{c:, …, c_r}D, with D fully determined and other parameters completely free, and where r is the observer order. This paper also asserts that only this set of linear equations can provide the unified upper bound of r, min{n, v:+…+v_p} or min {n-m, (v:-1)+..(v_p-1)}, for strictly proper or proper observers respectively, where n, m, p, and v: (i=1, …, p) are the plant order, number of outputs, number of inputs (state feedback signals), and descending order observability indexes, respectively. This upper bound is lower than all other existing ones and is the lowest possible general upper bound