Positive uncertain systems with one-sided robust control

We consider a control design problem for a class of uncertain systems. The salient features of the problem are fourfold. First, the uncertainty is time-varying. Second, the system is nonlinear. Third, the state is constrained to be only positive. Fourth, the control input may be constrained to be one-sided (i.e., either positive or negative). We start with a state transformation to release the state constraint. A partial sign-definiteness knowledge of the uncertainty is then shown to be critical to meet the control constraint. Three classes of controls are constructed: one for state constraint and two for the additional control constraint. They render the system globally practically stable.