  This paper provides new analytic tools for a rigorous control formulation and
stability analysis of sliding mode-multimodel controller (SM-MMC). In this way
to minimise the chattering effect we will adopt as a starting point the
multimodel approach to change the commutation of the sliding mode control (SMC)
into fusion using a first order then a high order sliding mode control with
single sliding surface and, then, with several sliding surfaces. For that the
stability conditions invoke the existence of two Lyapunov-type functions, the
first associated to the passage to the sliding set in finite time, and the
second with convergence to the desired state. The approaches presented in this
work are simulated on the immersion control of a submarine mobile which
presents a problem for the actuators because of the high level of system non
linearity and because of the external disturbances. Simulation results show
that this control strategy can attain excellent performances with no chattering
problem and low control level.

Systems and Control;Computational Engineering, Finance, and Science;Dynamical Systems;Optimization and Control