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.


93E11 Filtering in stochastic control theory
93E15 Stochastic stability in control theory
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