The Detectability of Time-Varying Differential-Algebraic Equations with Scalar Output

This paper considers time-varying linear and nonlinear systems of differentialalgebraic equations with a scalar observable output. In the linear case, sufficient detectability conditions are established, and a state observer is designed. For systems with a controlled input of a special form, a stabilization procedure using dynamic output feedback is proposed. Based on a linear approximation, detectability conditions are derived for a nonlinear system.