Optimal l/sub ∞/ to l/sub ∞/ estimation for periodic systems

Abstract

In this paper we consider the problem of finding a filter that minimizes the worst-case magnitude ( e, ) of the estimation error in the case of linear periodically time-varying systems subjected to unknown hut magnitude-bounded ( e, ) inputs. These inputs consist of process and observation noise, and the optimization problem is considered over an infinite-time horizon. Lifting techniques are utilized to transform the problem to a time invariant el -model matching problem subject to additional constraints. Taking advantage of the particular structure of the estimation problem, it is shown how standard methods of Ci optimization, in particular the delay augmentation technique, can be suitably modified to solve this nonstandard problem.

Residual Generation for Discrete Time Periodic Systems Using Parity Space Approach

“…For fault detection of discrete-time periodic systems they are first converted to time invariant reformulation using equations (7) to (10). After conversion, check existence condition for disturbance decoupling by using (19) and if it is not satisfied then do SVD of disturbance matrices using (23).…”

“…Active vibration control of helicopters [5]- [8], Networked control systems [9], Mutirate sampled data systems [10], Satellite attitude control [11] are important examples of periodic systems. To achieve reliability and enhanced safety of such systems various fault detection problems have been discussed in literature.…”

Lmi Approach to Robust Filtering for Discrete Time-Delay Systems With Nonlinear Disturbances

“…For such cases, H ∞ filtering was introduced in 1989 [6], where the input signal is assumed to be energy bounded and the main objective is to minimize the H ∞ norm of the filtering error system. Other performance indexes introduced for systems with partially known noise information are l 2 -l ∞ (energy-to-peak) [7] and l 1 (peak-to-peak) [8], which have different physical meanings when used as performance indexes for filtering error systems.…”

A New Parameter-Dependent Approach to Robust Energy-to-Peak Filter Design

“…Following the celebrated Kalman filtering scheme [1], [15], H ∞ filtering [9], [29], [30], L 2 -L ∞ filtering (also referred to as energy-to-peak filtering) [14], and L 1 filtering (also referred to as peak-to-peak filtering) [23] were proposed in the last decade, aimed at providing state estimation strategies for systems with non-Gaussian noises where standard Kalman filtering is not applicable. These filtering strategies have been used in a variety of settings, such as uncertain systems [12], [21], time-delay systems [17], stochastic systems [6], [13], [16], [25], sampled-data systems [22], and multidimensional systems [7].…”