Novel looped functionals for sampled-data-based robust stabilisation of a class of nonlinear systems

This paper deals with robust stabilisation of a class of nonlinear sampled-data control systems using the so-called looped functional method. It is known that constructing a proper looped functional is responsible for less conservative stability criterion. This paper paves a new way to construct a looped functional inspired from the Wirtinger inequality. The constructed looped functional can produce an extra negative quadratic term in its derivative, leading to an enhanced stability criterion with both less conservatism and less decision variables. Based on the obtained stability criterion, suitable robust controllers can be designed to maximise the bounds on the nonlinearity that maintain the system stability. Simulation illustrates the efficiency of the proposed method.