Model reference adaptive control of linear time-varying plants

This paper addresses the problem of model reference adaptive control of continuous-time and time-varying linear of the form ẋ(t) = Θ(t)x(t) + Bu(t), when the state is accessible and with an input vector of the same dimension as the vector state. The proposed control scheme guarantees that the state of the plant, with bounded time-varying parameters, asymptotically converges to the state of the model reference. For the general case when there are 2n² unknown parameters (n² time-varying and n² constant), a controller adjusting n²+1 parameters (when the control matrix B is unknown) guarantees local stability results, whereas in the case when the control matrix B is known, only one parameter has to be adjusted in the controller and the proposed scheme provides global stability results.