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.

保证成本估计 (GCE) 和保证成本控制 (GCC) 的问题分别涉及设计状态观察器或控制器，以便将某些性能保持在上限以下。本文提供了一种基于矩阵不等式的观测器/控制器设计程序，以在受致动器饱和影响的一类非线性系统中执行 GCE 和 GCC。特别地，这类系统对应于那些在考虑零输入时状态空间的原点是平衡点的系统，并且非线性相对于状态是可微的，相对于饱和输入是线性的。使用数值示例和旋转单臂倒立摆获得的仿真结果用于说明所提出的设计程序的有效性。