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.