Adaptive stabilization of linear and nonlinear plants in the presence of large and arbitrarily fast variations of the parameters

The problem of adaptive stabilization of a class of continuous-time and time-varying nonlinear plants is treated in this paper. The control scheme guarantees that the state of the plant, with bounded time-varying parameters, asymptotically converges to zero. For the nonlinear case with n²+n unknown parameters (n time-varying and n² constant), when the control matrix B is unknown the controller has to adjust n²+1 parameters providing only local stability results. On the contrary, when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results. The general methodology is particularized for the linear case with 2n² unknown parameters (n² time-varying and n² constant), adjusting n²+1 parameters when the control matrix B is unknown and guarantees only local stability results, whereas in the case when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results.