In this paper, a decentralized dynamic sliding mode control (DySMC) strategy is applied to a multivariable level control system. The time derivative of the control input of the DySMC is considered a new control variable for an augmented system which is composed of the original system and the integrator. This DySMC can transfer discontinuous terms to the first-order derivative of the control input and effectively reduce the chattering. The interactions between input/output variables are a common phenomenon and a challenging task in the design of multi-loop controllers for interacting multivariable processes. For reducing the interaction among variables, ideal decouplers are used. Independent diagonal controllers are designed for each decoupled subsystem, which is reduced to the first-order plus dead-time (FOPDT) model. A numerical simulation test has been carried out on a reactor system of the Industrial-Scale Polymerization (ISP). Experimental tests are performed to check the efficacy of the proposed controller using a laboratory-level coupled tank system.  A comparison of the proposed approach and sliding mode controller (SMC) is presented. Simulation and experiment results show that the DySMC approach reduces the chattering, and compensates for the effect of the external disturbances, and parametric uncertainties.