“…with ∈ ℝ + being the learning rate, P ∈ ℝ n×n + is the unique solution to the Lyapunov equation 0 = A T r P + PA r + I n owing to A r being Hurwitz, and e s (t) ≜ x(t) − x ri (t) being the system error state vector for standard MRAC architecture. In addition,Ŵ s, max,i+( −1)n ∈ ℝ + denote symmetric elementwise projection bound defined such that |[Ŵ s (t)] i | ≤Ŵ s, max ,i+(j−1)n , *As it is known, 11,21,24 one needs to choose the nominal gain matrices K 1 and K 2 such that A r is Hurwitz and −EA −1 r B r = I m , where E ∈ ℝ m×n is a matrix that allows a user to select a subset of x(t) to be ideally followed by c(t). i = 1, … , n and j = 1, … , m. The following sufficient condition is needed for the stability of the standard MRAC architecture subject to actuator and unmodeled dynamics (see Section 3.1).…”