An invariance approach for sliding mode control design in nonlinear switched systems

This article presents a method for synthesizing sliding mode controllers in Single Input Single Output (SISO) switched nonlinear systems. The method, called the invariance control method, utilizes the invariance condition associated with each constant level set of the sliding surface coordinate function. It decomposes the SM control scheme into two parts: a smooth invariance feedback controller and a Delta-Sigma modulator. The smooth invariance feedback controller represents the equivalent control in a specific case, while the Delta-Sigma modulator provides the required binary-valued input signal to the switched plant based on the output of the invariance controller. The method can be applied to differentially flat systems with switched inputs, using linear, self-compensating sliding surface coordinate functions. The approach aligns with the Active Disturbance Rejection Control scheme for the average system but incorporates a Delta-Sigma modulator. The article showcases the method’s effectiveness through digital computer simulations and laboratory experiments with non-trivial application examples.