Jordan canonical form in diagnosis and estimation problems

We propose a method for solving diagnosis and estimation problems based on the Jordan canonical form. The problems of constructing diagnostic observers, virtual sensors, and interval and sliding-mode observers are considered. Algorithms for solving these problems are designed for both linear and nonlinear systems in the presence of exogenous disturbances and measurement noise. It is shown that in some cases, the use of the Jordan canonical form reduces the complexity of the observers and sensors and simplifies the procedure for their synthesis compared with the identification canonical form. This is illustrated by a practical example.