State estimation methods for lumped parameter systems are presented in the paper with application for robust control. All the methods are based on a nonlinear predictor, which estimates future states through state evolution computations. The prediction may be made in several successive steps or in one step as limit of multistep computations. The nonlinear estimator is a predictor -corrector type one, correction is made through optimization on a finite horizon, giving possibility for approximate minimum variance estimation for a class of nonlinear plants. At the same time, the presented predictor may replace the predictor of extended Kalman filter, making possible better prediction and overall estimation through modification of the extended Kalman filter algorithm. An example shows how to design robust nonlinear stochastic control with the original nonlinear model and with the nonlinear estimator presented in the paper for a class of nonlinear plants. The solution is achieved in analytical form