Global Multivariable HOSM Differentiator for Output-Feedback Unit Vector Control of Nonuniform Relative Degree Systems

In this paper, we propose an output feedback unit vector controller to solve the longstanding problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to deal with the nonuniform arbitrary relative degree, we extend our previous estimation scheme based on global differentiators using dynamic gains to a multivariable framework. A diagonally stable assumption over the system high-frequency gain (HFG) matrix must be invoked. Preserving the same guidelines and simplicity of its monovariable version, the variable gain super-twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. In addition, norm observers for the unmeasured state are employed to dominate the disturbances as well as to update the differentiator gains since both may be state dependent. Thus, uniform global exponential stability and ultimate exact tracking are guaranteed. A numerical example is presented to illustrate the application of the proposed multivariable approach.