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Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters. (English) Zbl 0986.93066

The authors consider the problem of Kalman filtering for a class of uncertain linear continuous-time systems with Markovian jumping parameters described by

x ˙(t)=[A(r(t))+ΔA(t,r(t))]x(t)+w(t),x(0)=x 0 ,r 0 =i,
y(t)=[C(r(t))+ΔC(t,r(t))]x(t)+v(t),

where x n and y m are the state and measurement vectors, respectively; w n and v m are the state and measurement noises, respectively; A(r(t)), ΔA(t,r(t)), C(r(t)) and ΔC(t,r(t)) are matrices of appropriate dimensions; {r(t),t0} represents a homogeneous continuous-time discrete-state Markov process taking values in a finite set S={1,2,,s} with stationary transition probabilities. For each r(t)S, ΔA(t,r(t)) and ΔC(t,r(t)) represent the system’s uncertainties.

The authors design a stochastic quadratic estimator that guarantees both the stability and boundedness of the estimation error dynamics.

MSC:
93E11Filtering in stochastic control
93E15Stochastic stability