Necessary and sufficient conditions for normalization and sliding mode control of singular fractional-order systems with uncertainties

The sliding mode control (SMC) problem for a normalized singular fractional-order system (SFOS) with matched uncertainties was investigated. Firstly, SFOS was normalized under constrained conditions. Then, the linear sliding mode (SM) function was designed using a fractional-order (FO) positive definite matrix and a linear matrix inequality (LMI). The SM controller was subsequently constructed based on switching laws. Finally, the feasibility of the method was evaluated using a numerical example.