A direct algebraic approach to observer design under switching measurement equations

Based on the algebraic transformation of a switched linear measurement equation into a nonlinear, yet deterministic, equation, an asymptotic state observer is constructed for discrete-time linear systems whose observations are generated according to randomly switching measurement modes. The observer, which combines the algebraic transformation with a Newton observer applied to the resulting nonlinear measurement equation, is shown to be locally exponentially convergent under arbitrary mode sequences.