Output integral sliding mode control based on algebraic hierarchical observer

The problem of the realization of integral sliding mode controllers based only on output information is discussed. The implementation of an output integral sliding mode controller ensures insensitivity of the state trajectory with respect to the matched uncertainties from the initial time moment. In the case when the number of inputs is more than or equal to the number of outputs, the closed loop system, describing the output integral sliding mode dynamics, is shown to lose observability. For the case when the number of inputs is less than the number of outputs, a hierarchical sliding mode observer is proposed. The realization of the proposed observer requires a filtration to obtain the equivalent output injections. Assigning the first order low-pass filter parameter small enough (during this filter realization), the convergence time and the observation error can be made arbitrarily small. The results obtained are illustrated by simulations.