Stability analysis of a model reference adaptive control system with sinusoidal inputs†

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Abstract
In this paper a rigorous method is presented for analysing an M.I.T. type model reference adaptive control system with sinusoidal inputs. The linearized equations for the adapting system, formed by using small perturbation analysis, are written in the matrix form [xdot] = A(t)x, where A(t) is periodic. This matrix equation is then integrated over one period using a Runge–Kutta technique. The transition matrix relating the value of x at the end of a period to its value at the beginning of the period is examined to see whether all its eigenvalues are within the unit circle, thus establishing stability.

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