Suppose a discrete-time linear system P as in Fig 1, is described by some unknown dynamics that you would like to identify to later design a controller for. A colleague has conducted an experiment and collected a set of noisy data (ui, yi) where ui,yi are the input and the output of the system P at k = i, respectively. The output is the full-state vector xk of the system corrupted by some noise wk. Assume that the collected data come from a model described by the following equation xk+1 = a0xk + b0uk (1) yk = xk + wk (2) where a0 and b0 are the unknown parameters of the system P and wk is i.i.d N (0, 1). Given the set of data (uk, yk) for k = 0, 1, ...n and assuming we start the system at rest, rewrite the previous form as yk+1 = T k + wk+1, k = 0, 1, ..., n 1