In this paper an attempt is made to extend the concept of the exponentially stable adaptive control to one class of MIMO systems with matched nonlinearity and unknown piece-wise constant parameters. Within the intervals between parameter switches, the proposed adaptive control system provides: 1) the monotonicity of the control law adjustable parameters, 2) exponential convergence to zero of the reference model tracking and parameter errors. Both properties are guaranteed in case a finite excitation requirement is met for the regressor inside each of such intervals. Compared to the existing methods, the proposed one is applicable to systems with unknown both switching signal function and control matrix. The numerical experiments validate the theoretical results.