The problem of H∞ filter design for continuous-time nonlinear polynomial systems is addressed in this paper. The aim is to design a full order dynamic filter that depends polynomially on the filter states. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H∞ performance bound for the augmented polynomial system, composed by the original ...

Multichannel or multi-input multi-output multirate filtering is discussed in this paper. Vector multirate systems are defined, and the issues of aliasing cancellation and perfect reconstruction are addressed in the vector context. The conditions for a vector linear periodically time-variant system to become time-invariant are derived. The idea of doubly complementary filters is generalized to t...

Answer: The purpose of introducing a constant matrix X in Theorem 2 is to make a decoupling between the matrix function P (ri,j) and the system dynamic matrices in Theorem 1. This decoupling technique enables us to obtain a more easily tractable condition for the filter synthesis. Therefore, the matrix X cannot be selected to be parameter-dependent. It seems that some conservatism will be intro...

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are projected onto Gaussian distributions. Here, we offer an important generalization to the case where er...

Matrix inversion is routinely performed in computational engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot–Jacobi (also known as the ‘‘Lewis Carol’’) identity shows how the determinan...

A theory for optimal filtering of infinite sets of random signals is presented. There are several new distinctive features of the proposed approach. First, a single optimal filter for processing any signal from a given infinite signal set is provided. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Ea...

The speech enhancement is one of the important techniques used to improve the quality of a speech signal i.e. degraded by noise. Speech enhancement using conventional kalman filter require calculating the parameters of AR (auto-regressive) model, and performing a lot of matrix operations, which is non-adaptive. In this paper the proposed method i.e. adaptive kalman filter combined with perceptu...

We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each ...

In this paper, a decentralized information filter in federated structure is developed in multi-sensor environments. Being equivalent to the Kalman filter algebraically, the information filter of Mutambara 11) is extended to N -sensor distributed dynamic systems. In multi-sensor environments, the information-based filter is easier to decentralize, initialize, and fuse than a KFbased filter. The ...