  Phasor measurement units ({PMUs}) have become instrumental in modern power
systems for enabling real-time, wide-area monitoring and control. Accordingly,
many studies have investigated efficient and robust dynamic state estimation
(DSE) methods in order to accurately compute the dynamic states of generation
units. Nonetheless, most of them forego the dynamic-algebraic nature of power
networks and only consider their nonlinear dynamic representations. Motivated
by the lack of DSE methods based on power network's differential-algebraic
equations (DAEs), this paper develops a novel observer-based DSE framework in
order to perform simultaneous estimation of the dynamic and algebraic states of
multi-machine power networks. Specifically, we leverage the DAE dynamics of a
power network around an operating point and combine them with a PMU-based
measurement model capable of capturing bus voltages and line currents. The
proposed $\mathcal{H}_{\infty}$ observer, which only requires detectability and
impulse observability conditions which are satisfied for various power
networks, is designed to handle various noise, unknown inputs, and input sensor
failures. The results obtained from performing extensive numerical simulations
on the IEEE $9$-bus and $39$-bus systems showcase the effectiveness of the
proposed approach for DSE purposes.
