H∞ control of nonlinear sampled-data systems

This paper investigates the H_∞ control problem for a class of nonlinear sampled-data systems which are affine in the inputs. Sufficient conditions for the existence of a digital controller that guarantees the L₂ gain from an exogenous input to a controlled output is less than or equal to a prescribed value are obtained. Those conditions are expressed in terms of both continuous and discrete Hamilton-Jacobi equations. Then we extend this result to nonlinear sampled-data systems with uncertainties which are described by some integral functional constraint. It is shown that robust H_∞ control problem can be solved via a scaled nonlinear sampled-data system without uncertainties. Solutions to the latter problem are also presented