Reduced-order functional observers for descriptor linear time-invariant systems: a parametric method

This article introduces the parametric design method of the reduced-order functional observer for descriptor linear time-invariant systems. First, existence conditions of reduced-order functional observers are provided. Then, based on the solution of generalized Sylvester equations, completely parameterized expressions of the coefficients matrices of the reduced-order functional observer are established, and the design algorithm of the reduced-order functional observer is also proposed. The advantage of the proposed design method is that the observation error system can be transformed into a linear system with an expected eigenstructure. Finally, two examples are given to verify the effectiveness of the proposed method.