Terminal sliding mode decomposed control of multivariable linear uncertain systems

A terminal sliding mode decomposed control method for a linear multivariable system with unmatched uncertainties is proposed. The system was converted into the block controllable form consisting of two parts, the range space subsystem with matched uncertainties and the stable zero-dynamic subsystem with unmatched uncertainties. The special terminal sliding mode was presented for the range space subsystem, and the control law was designed to drive the state variables of the range space subsystem to the equilibrium points within a finite time. Then, the state variables of the zero-dynamics converged to the neighborhood of equilibrium points asymptotically, and the mathematical relationship with the range of the unmatched uncertainties was formulated. Simulation results were presented to validate the design and the analysis. The mathematical relationship can be used for the system design and analysis. The proposed method is significant for high-dimensional linear multivariable systems with unmatched uncertainties in that it can simplify the design of controller and realize the hierarchical control.