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 'averaged' 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 'averaging concept' applied within the frame of stochastic Lyapunov-like analysis. The stochastic calculus (It@ 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 high-gain 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.