Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates

This paper deals with the model reference tracking control problem of linear systems based on the observer for Markov jump systems with unknown transition rates. The main contributions are as follows: Firstly, we designed a descriptor observer for a given model by the matrix transformation. Then, a tracking control law composed of a feedforward compensator and feedback control law was designed by calculating variations based on the designed observer. The feedback part can stabilize the system. The feedforward part is the complete parametric feedforward tracking compensator. The two parts can be solved separately, and a controller that can make the system stable is proposed under the condition that transition rates are partially unknown through the Lyapunov stability theory. The feedforward parametric solution is given by the generalized Sylvester equation. The algorithm and criteria are proved by several examples and compared with the existing conclusions.

Automated summary

This paper tackles the issue of model reference tracking control for linear systems based on the observer in the context of Markov jump systems with unknown transition rates. The main contributions include the design of a descriptor observer using matrix transformation and the formulation of a tracking control law utilizing a feedforward compensator and feedback control. The stability of the system is ensured by the feedback component, while the feedforward component serves as a complete parametric tracking compensator. Both components are solved separately, and a controller is proposed under the condition of partial unknown transition rates using Lyapunov stability theory. The feedforward parametric solution is provided through the generalized Sylvester equation. The effectiveness of the algorithm and criteria is demonstrated through various examples and compared with existing findings.