Sliding mode control for systems with zero-crossing control gain under matched and mismatched disturbances

The robust control problem for systems with control coefficients without a constant sign and not separated from zero is addressed. It is shown that persistence of excitation conditions for the modulus of the control gain are sufficient to ensure stability of the system and matching conditions for the disturbance are sufficient to ensure finite -time stability, in the discontinuous case. Additionally, it is shown that finite -time convergent homogeneous controllers can guarantee uniform ultimate boundedness of the solutions even in the presence of mismatched disturbances and persistence of excitation conditions for the modulus of the control gain. (c) 2023 Elsevier Ltd. All rights reserved.