A new control method and its robustness for a class of nonlinear systems
For a class of time-varying nonlinear systems described by the equation ẋ\(=f(x,t)+g(x,t)u\), the precalculating control is not available if the input matrix g(x,t) is not invertible. With Lyapunov's second method, a stabilizing controller which makes the system practically stable is constructed. It is shown that the implementation of this scheme depends on some so-called posi-invertibility conditions for g(x,t). In case the system is partly stable, the method, named part-calculating control, can simplify the on-line computations. Without the assumption that the nominal system is asymptotically stable, the method is applied to the problems of control for the corresponding uncertain system which satisfies the matching condition. When the matching condition is not satisfied, the mismatching control problem is also studied with Lyapunov's second method.
scientific article; zbMATH DE number 4027294
scientific article