Abstract
This paper deals with a design of a adaptive controller with adjustments working in sliding mode. The mathematical description of the plant is linear continuous single input model. The structure of the adaptive law is chosen linear. Stability problem of the closed loop equation is solved using second method of Lyapunov with the LaSalle‘s extension. It is shown that the stability problem leads to the ‘Normal equations’ in closed loop, but here in differential form. They are solved as optimisation problem by sliding mode technique. The stochastic case in the presence of Gauss white noise is investigated using again the second method, but with stochastic Lyapunov function. Numerical simulations are also carried out.
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