Observer design in matrix second order system framework; measurement conditions and perspectives

In this paper, we introduce the conditions for the existence of the second order observer gains directly in the matrix second order framework to synthesize observer gains taking various assumptions on available measurements into consideration. Several important reasons are presented to justify the need for this approach and the advantages of the second order observer are explained and contrasted with those of the typical first order observer. This concept of direct matrix second order framework design is new and attractive, especially for observer based controllers.