Stochastic output noise effects in sliding mode state estimation

This paper is devoted to the analysis of effects of stochastic output noises acting on a stochastic continuous time system which states are estimated using mixed (linear and sliding-mode type) observers. Such observers provide the stable (with probability one) estimates. The ʹaveragedʹ norm of estimation error converges to a zone where size is proportional to the acting noise power. The main technique of the proof is based on the ʹaveraging conceptʹ applied within the frame of stochastic Lyapunov-like analysis. The stochastic calculus (Itô formula) as well as some basic principles for stochastic processes are used to obtain the convergence results. The size of the obtained zone is analysed as a function of the sliding mode gain parameter. It is shown that the sliding mode term helps a highgain linear observer to make this zone smaller. The illustrative example dealing with the circuit of a full bridge boost type PFP (power factor precompensator) concludes this study.