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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 $$\dot x(t)= [A(r(t))+\Delta A(t, r(t))] x(t)+ w(t),\quad x(0)= x_0,\quad r_0= i,$$ $$y(t)= [C(r(t))+\Delta C(t, r(t))] x(t)+ v(t),$$ where $x\in \bbfR^n$ and $y\in \bbfR^m$ are the state and measurement vectors, respectively; $w\in \bbfR^n$ and $v\in \bbfR^m$ are the state and measurement noises, respectively; $A(r(t))$, $\Delta A(t, r(t))$, $C(r(t))$ and $\Delta C(t, r(t))$ are matrices of appropriate dimensions; $\{r(t), t\ge 0\}$ represents a homogeneous continuous-time discrete-state Markov process taking values in a finite set $S= \{1,2,\dots, s\}$ with stationary transition probabilities. For each $r(t)\in S$, $\Delta A(t,r(t))$ and $\Delta C(t, r(t))$ represent the system’s uncertainties. The authors design a stochastic quadratic estimator that guarantees both the stability and boundedness of the estimation error dynamics.

93E11Filtering in stochastic control
93E15Stochastic stability
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