In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation.

This paper proposes a general method for dealing with state estimation under nonlinear state soft inequality constraints. This method is based on the projection approach, and then has the advantage to be compatible with any kind of state estimator. In order to be taken into account, the nonlinear constraints are linearized about the constrained state using an iterated approach. The proposed algorithm is tested on a threedimension tracking application with nonlinear constraints on the moving body acceleration. The results are compared with those of an unconstrained Kalman filter. This work was supported by the French arming delegation (DGA) V. Sircoulomb, G. Hoblos and H. Chafouk are with the engineering school ESIGELEC,

This paper addresses the problem of designing a classical observer extended to dynamical discrete-time systems with constant delays. The idea of two forms of state observers is presented to compensate fixed time-delay. Convergence conditions have been found to ensure the stability of the error dynamics and the related gains may be selected based on a set of linear matrix inequality (LMI). The results show that the compensation-based state observer is much superior in dealing with time-delay in the case that the buffer permits us to transform the time-delay system into a fixed time-delay system. Simulation and experimental results are provided to demonstrate the advantage of the proposed observation technique.

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With regards to the characteristics of uncertain long delay of networked control system (NCS), the stochastic time-delay system can be transformed to a deterministic delay system by placing proper quantities of buffers at the nodes of the double-end networked control systems. An observer-based control design subject to fixed time delay is proposed to construct the augmented state-space model. Based on the Lyapunov function and linear matrix inequality (LMI) theorem, sufficient and necessary conditions for stability of such systems using static state feedback are given. Simulation result proves its effectiveness.

This paper presents a method for dealing with Kalman filtering under particular classes of nonlinear state model and state inequality constraints. This method is based on a modification of the optimal Kalman gain in order to enforce the state constraints if necessary. The proposed method is applied to a nonlinear hydraulic system in order to highlight the efficiency of this method.

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