Analysis of linear systems in the presence of actuator saturation and L2-disturbances

This paper presents a method for the analysis and control design of linear systems in the presence of actuator saturation and L₂-disturbances. A simple condition is derived under which trajectories starting from an ellipsoid will remain inside an outer ellipsoid. The stability and disturbance tolerance/rejection ability of the closed-loop system under a given feedback law is measured by the size of these two ellipsoids and the difference between them. Based on the above mentioned condition, the problem of estimating the largest inner ellipsoid and/or the smallest difference between the two ellipsoid is then formulated as a constrained optimization problem. All the constraints are shown to be equivalent to LMIs. In addition, disturbance rejection ability in terms of L₂ gain is also determined by the solution of an LMI optimization problem. By viewing the feedback gain as an additional free parameter, the optimization problem can easily be adapted for controller design. Numerical examples show that the proposed analysis and design methods significantly improve recent results on the same problems.