Guaranteed cost estimation and control for a class of nonlinear systems subject to actuator saturation

The problems of guaranteed cost estimation (GCE) and guaranteed cost control (GCC) concern designing a state observer or a controller, respectively, such that some performance is maintained below an upper bound. This paper provides a matrix inequality-based observer/controller design procedure to perform GCE and GCC in a class of nonlinear systems affected by actuator saturation. In particular, this class of systems corresponds to those for which the origin of the state space is an equilibrium point when null inputs are considered, and the nonlinearity is differentiable with respect to the state and linear with respect to the saturated input. Simulation results obtained using a numerical example and a rotational single-arm inverted pendulum are used to illustrate the effectiveness of the proposed design procedure.