Chattering-Free Second Order Robustness Sliding Mode Controller for Complex Interconnected Systems: A Moore-Penrose Inverse Technique

In this paper, a novel second order sliding mode control approach is extended toa class of complex interconnected systems with mismatched interconnections and unknown perturbations. The key contribution of this paper is to cancel two common restrictions clogging the application of the variable structure control to complex interconnected systems: 1) all of state variables must be accessible; 2) the control input is affected by chattering problems. First, a novel reduced-order sliding mode estimator (ROSME) is proposed to estimate the unmeasurable variables. Second, based on Moore-Penrose inverse technique and ROSME tool, a new decentralized chattering-free second order robustness sliding mode controller (CSORSMC) is developed to force the system states to stay in a sliding surface from the initial period instance and attenuate the chattering phenomenon in the control signal. Besides, a novel appropriate linear matrix inequality (LMI) requirement is proved such that the plant in sliding mode is asymptotically stable. Lastly, a mathematical model including two subsystems is simulated which confirms the usefulness and advantages of proposed technique.