Constraining the output of discrete-time systems using sliding mode control with a novel sliding hyperplane

Sliding mode control strategies are widely applicable to systems subject to disturbance and modeling uncertainties. However, since sliding mode controllers are typically only concerned with the evolution of a virtual sliding variable, potential state constraints placed on the system are often neglected when applying such strategies. Motivated by this problem, in this article, we propose a novel sliding mode control strategy for discrete-time systems with the aim of satisfying constraints placed on their output. The proposed approach uses a new sliding hyperplane designed to ensure a linear relationship between the sliding variable and the system output. The main contribution of the article involves demonstrating that when using this approach, one can indirectly impose bounds on the output rate of change by limiting the convergence rate of the sliding variable to zero. The obtained result has been documented for two cases. In the first part of the article, the proposed approach has been applied to systems with full state information always known. Then, the strategy has been extended to plants with only output signal available, where the full state needs to be estimated.