Multi-scale Fusion Of Multi-rate Systems And The Stability Analysis Of Uncertain Systems

In multi-rate signal processing, several sensors are used to observe the system, how to combine the different type sensors on different scales and how to utilize the observation to obtain the effective fusion is a research aspect, while multi-scale analysis and multi-scale modeling is an important research aspect.With the development of the multiscale theory, it has been intensively suggested to combine the wavelet analysis with Kalman filter and use it to effectively estimate the multi-rate system research and application attract more and more attention. With the real time estimate property of Kalman filter and the multi-scale ability, new algorithm can be used to analyze the statistic property of object on different scales, based on which the multiscale form of the object is expressed to obtain the effective, parallel recursive algorithm. The key to realize the object is accurate multi-scale modeling and finding the effective fusion algorithm, which is an important manner to obtain the multi-scale data analysis and signal processing.This paper use a new parting technology and multi-scale transform method to found a new dynamic system based on time-frequency domain. This paper gives the recursive multi-scale data fusion algorithm of the system with single sensor single model and multi-sensor single model, respectively. With single sensor, first, reformulate the original state and measurement dynamic systems in a new blocked data form, then the multi-scale model is founded based on the multi-transform, last, adopt the main idea of Kalman filter to develop the new algorithm. The difference of multi-sensor is that it combines the idea of sequential filtering to obtain optimal hybrid state estimator in the multiscale domain. These algorithms are real-time, recursive.In the other part of this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with time delay and missing measurements using the constrained method of estimate error covariance. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The probability of the occurrence of missing data is assumed to be known and assumed to be a Bernoulli distributed white sequence. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities and quadratic matrix inequalities and obtain an effective condition of the system stability.