Parametric design of functional observer for second‐order linear time‐varying systems

Abstract

AbstractThis note constructs a functional observer for second‐order linear time‐varying (SOLTV) systems under framework of second‐order systems. Based on the assumption that the SOLTV system is observable, sufficient conditions for the existence of a second‐order functional observer are proposed. Combined with the solution of generalized Sylvester equation (GSE), the completely parameterized expressions of coefficient matrices of functional observer are proposed, which includes the free parameters representing degrees of freedom, and can be utilized to achieve some additional performance. Further, the design procedure is put forward, whose validity is verified through an example.