Decentralized variable structure control design in perturbed nonlinear systems

This paper presents a new robust decentralized variable structure control (DVSC) to stabilize a class of perturbed nonlinear large-scale systems. Only the bounds of perturbations, disturbances and interconnections of the system are needed. Based on Lyapunov theory, the DVSC is designed such that a Lyapunov function converges to a composite switching hyperplane in finite time, at least with an exponential rate. Our design method need not use the dynamic compensation or the integral of interconnections in the sliding mode definition, or the hierarchical control. Furthermore, both the convergence rate and the hitting time can be assigned. Finally, a two-pendulum system is given to illustrate the design method.