In this paper, we propose a robust state estimation method using a particle filter (PF) for a class of nonlinear systems which have stochastic parameter uncertainties. A robust PF was designed using prediction and correction structure. The proposed PF draws particles from a simple proposal density function and corrects the particles with particle-wise correction gains. We present a method to obtain an error variance of each particle and its upper bound, which is minimized to determine the correction gain. The proposed method is less restrictive on system nonlinearities and noise statistics; moreover, it can be applied regardless of system stability. The effectiveness of the proposed robust PF is illustrated via an example based on Chua's circuit.

In this paper, we propose a new modeling method to express discrete-time hybrid systems with parameter uncertainty as a mixed logical dynamical (MLD) model. In analysis and control of hybrid systems, there are problem formulations in which convex polyhedra are computed, but for high-dimensional systems, it is difficult to solve these problems within a practical computation time. The key idea of this paper is to use an interval method, which is one of the classical methods in verified numerical computation, and to regard an interval as an over-approximation of a convex polyhedron. By using the obtained MLD model, analysis and synthesis of robust control systems are formulated.

A new robust extended Kalman filter is proposed for the discrete-time nonlinear systems with norm-bounded parameter uncertainties. After linearization of the nonlinear systems, the uncertainties described by the energy bounded constraint can be converted into an indefinite quadratic cost function to be minimized. The solution to the minimization problem is given by the extended Kalman filter derived in a Krein space, which leads to a robust version of the extended Kalman filter. Since the resulting robust filter has the same structure as a standard extended Kalman filter, the proposed filter can be readily designed by simply including the uncertainty terms in its formulas. The results of simulations are presented to demonstrate that the proposed filter achieves the robustness against parameter variation and performs better than the standard extended Kalman filter.

This paper provides a new robust guaranteed cost controller design method for discrete parameter uncertain time delay systems. The result shows much tighter bound of guaranteed cost than that of existing paper. In order to get the optimal (minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) technique. Also, the parameter uncertain systems with time delays in both state and control input are considered.