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Robust H filtering of stationary continuous-time linear systems with stochastic uncertainties. (English) Zbl 1016.93067

The authors consider the following linear mean-square stable system

dx=(Ax+B 1 w)dt+Dxdβ,dy=(Cx+B 2 w)dt+Fxdζ,z=Lx,

where x n is the system state vector, y r is the measurement, z m is the state combination to be estimated, β and ζ are Wiener processes, w is the disturbance signal satisfying

0 Ew(t) 2 dt<,w(t) q ,

and all the matrices are constants and of the appropriate dimensions. They consider the following filter for the estimation of z(t):

dx ^=A f x ^dt+B f dy,z ^=C f x ^,

and invstigate the stochastic H filtering problem: given γ>0, find an asymptotically stable linear filter of the above form that leads to an estimation such that

J:= 0 Ez(t)-z ^(t) 2 dt-γ 2 0 Ew(t) 2 dt

is negative for all nonzero w.

MSC:
93E11Filtering in stochastic control
93C73Perturbations in control systems
93B36H -control