Hybrid filtering for linear systems with non-Gaussian disturbances

Design of Observers for Hybrid Systems

“…Subsequently, state estimation was considered by several authors in a probabilistic framework (see e.g. [17]). Gain switching observers for nonlinear systems were studied in [8].…”

On reference model tracking for Markov jump systems

“…In Wang, Qiao and Burnham (2002), the stabilisation problem for the class of Markovian jump systems with time-delay and external disturbance has been tackled and solved using the LMI setting. Results on filtering can be found in Zhang (2000) and Boukas (2005). In Boukas and Liu (2001) and Sethi and Zhang (1994), the framework of the class of Markovian jump systems has been used in manufacturing systems with random breakdowns to deal with the production and maintenance planning.…”

“…But practically, this is not always possible since the mode is not always accessible and neither is the instant of the switch, which restricts the use of such controllers. It is possible to estimate the mode as it was done by Zhang (2000) and therefore continue to use the controller. But if we are interested by real-time applications then this is not possible unless the size of the system is small.…”

Robust linear filtering for discrete-time hybrid Markov linear systems

“…This class of system is known as Markovian jump linear systems (MJLS). When only an output of the system is available, and therefore the values of the jump parameter are not known, the problem of optimal and sub-optimal ®ltering has been addressed in Ackerson and Fu (1970), Chang and Athans (1978), Tugnait (1982 a, b), Blom and BarShalom (1988), Bar-Shalom and Li (1993) and Dufour and Elliott (1997) among other authors, under the hypothesis of Gaussian distribution for the disturbances, and by Zhang (1999Zhang ( , 2000 for the nonGaussian case. Since the optimal estimator requires exponentially increasing memory and computation with time, sub-optimal algorithms are required.…”