ℋ︁_∞ filtering for discrete‐time linear systems with Markovian jumping parameters†

Abstract

SUMMARYThis paper investigates the problem of H 1 filtering for discrete-time linear systems with Markovian jumping parameters. It is assumed that the jumping parameter is available. This paper develops necessary and sufficient conditions for designing a discrete-time Markovian jump linear filter which ensures a prescribed bound on the ' 2 -induced gain from the noise signals to the estimation error. The proposed filter design is given in terms of linear matrix inequalities.

Fixed Interval Optimal Estimation for Linear Discrete-Time Markovian Jump Systems by Maximum Likelihood Approach

“…Note that, for the Markovian jump systems, the filter dynamics are uncoupled with each other, but the smoother dynamics are coupled with each other, while the Riccati difference equations, by the solutions of which the filter and smoother gains are determined, are coupled with each other. Also note that the coupled Riccati difference equations obtained in this paper is rather natural both in the meaning that they are an extension of the Riccati equation for the single mode systems and in the meaning that they are a limit from the Riccati equations for H ∞ state estimation as a disturbance index γ to ∞ compared the references [7,27,29] and so on.…”

“…Markovian jump systems ( [4,5,6,7,8,9,10,11,14,15,17,18,25,26,27]) have abrupt random mode changes in their dynamics. The mode changes follow Markov processes.…”

“…Such systems may be found in the area of power systems, manufacturing systems, communications, aerospace systems, financial engineering and so on. Such systems are classified into continuoustime ( [5,8,10,11,15,17,25,26]) and discrete-time ( [4,6,7,9,14,18,27]) systems. The optimal and H ∞ control theory has presented for each of these systems respectively ( [7,9,15,25]).…”

“…The optimal and H ∞ control theory has presented for each of these systems respectively ( [7,9,15,25]). With regard to the estimation for the Markovian jump systems, the LMMSE filtering theory ( [6,7,11]), the approximately optimal smoothing theory ( [4,14]) and the H ∞ filtering theory ( [26,27]) in terms of LMIs have been presented.…”

“…In [27], the H ∞ filtering theory for linear discrete-time Markovian jump systems has been already presented in terms of LMIs. However the direct derivation method of coupled Riccati difference equations and the relationship between filtering and smoothing theory have not been fully investigated for the systems.…”