Controller design for nonlinear systems in its general form is complicated and an open problem. Finding a solution to this problem becomes more complicated when unwanted terms, such as disturbance, are taken into account. To provide a robust design for a subclass of nonlinear systems, sliding mode controllers (SMCs) are used. These controllers have a systematic design procedure and can reject bounded disturbances and at the same time guarantee stability. The guaranteed stability is achieved by separating system states into two parts and assuming that the input to state stability (ISS) condition holds for internal dynamics. This condition restricts the applicability of the SMC and limits the system performance when the controller is designed based on that. In order to remove this restriction and improve the performance, the ISS condition has been relaxed in this study. The relaxation is performed by redesigning SMCs based on suggested Lyapunov functions. The proposed idea insures global asymptotic stability of the closed loop system and is used to revise different well-known SMCs such as conventional SMC, terminal SMC, non-singular terminal SMC, integral SMC, super-twisting SMC, and super-twisting integral SMC. Comparisons between conventional and revised versions are made using simulation to demonstrate excellence of the revisited controllers.
Pareto Design of Decoupled Sliding-Mode Controllers for Nonlinear Systems Based on a Multiobjective Genetic Algorithm