of the matrix d are the same and the first two elements of the matrix d are zero and the like different buildings with different geometries and input and output data have different thermal rc networks and thus different constraints 307 given an input output sequence of data such that u u 0 u 1 u n 2k u2212 2 and y y 0 y 1 y n 2k u2212 2 hankel matrices u p u f y p yf are given the lti system according to equation 1 the observability matrix o k and the toeplitz matrix u03c8 k are respectively using the state transition relation in equation 1 the state sequence x f of the lti system given the input sequence u f and measurements y f are y f r 31 u2212 r 32 r 22 u2020 r 21 r 11 u2212 1 u f r 32 r 22 u2020 w p 10 where u2020 represents the pseudo inverse of a matrix then using equation 8 and equation 10 o k x f r 32 r 22 u2020 w p 11 using a singular value decomposition svd and the arbitrary invertible matrix u03c6 see equation 3 equation 11 reduces to thus for a given user parameter k see equation 6 there can be many different realizations of the state sequences arising from the same lti system based on different values of the matrix u03c6 the method.