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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 $$x\in \mathbb{R}^n$$ and $$y\in \mathbb{R}^m$$ are the state and measurement vectors, respectively; $$w\in \mathbb{R}^n$$ and $$v\in \mathbb{R}^m$$ 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; $$\{r(t), t\geq 0\}$$ 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.

##### MSC:
 9.3e+12 Filtering in stochastic control theory 9.3e+16 Stochastic stability in control theory
##### Keywords:
Kalman filtering; Markovian jumping parameters
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