Robust Nonlinear Control of Singular Systems with Saturating Actuator Constraint

Solving the robust regulation problem is considered for singular systems in the presence of actuator saturation, model uncertainties, and disturbances. Although singularity of system equations, caused by existence of algebraic equations together with differential ones, gives it a great ability for describing more precise behaviors of dynamical systems, it also causes complexities in analysis and design procedures. On the other hand, considering actuator saturation constraint as a practical limitation for the system needs precise mathematical calculations. In this regard, a theorem is given that shows the proposed robust control law is capable to drive the output of the system to track a step reference in presence of uncertainties, disturbances, and actuator saturation constraint. Investigating different cases of saturation function with precise mathematical operations in the given theorem based on Lyapunov approach analysis demonstrates that the regulation goal is achieved even if the input saturation takes place. The accuracy of the proposed control law is finally verified by computer simulations.