Robust Sliding Mode Techniques for Control and State Estimation of Dynamic Systems with Bounded and Stochastic Uncertainty

Bounded and stochastic disturbances form a very important impact on system models in general. The consideration of these in control and observer strategies is a challenge for researchers. The problem is that common control procedures may depend on special properties of the system. Often, procedures for linear system models cannot be used for nonlinear ones. In this contribution, sliding mode techniques are further developed for control and estimation tasks such that the principle procedure is not limited to linear systems. To consider uncertain but bounded parameters and stochastic disturbances simultaneously, intervals are introduced in the resulting stochastic differential equations. Additionally, stability of the presented procedures can be guaranteed by involving the Itˆ o differential operator and linear matrix inequalities to obtain sliding mode strategies for robust control and estimation tasks in combination with interval arithmetic.