Abstract
This paper investigates model reference control for linear time-varying (LTV) systems. It is shown that the problem can be decomposed into two sub-problems: a state feedback stabilization problem of LTV systems and a feed-forward compensation problem. Firstly, the sufficient condition for the existence of the model reference control is deduced. The condition concerns two coefficient matrices such that two matrix equations are met simultaneously, and the state feedback gain matrix stabilizes LTV systems according to the unified spectral theory. Secondly, generally complete parametrization of the model reference tracking controller including a state feedback controller and a feed-forward compensator is proposed based on the solution to a type of generalized Sylvester matrix equations. Furthermore, a general procedure for solving the model reference control problem is also provided. Finally, a numerical example shows the feasibility and effectiveness of the parametric design approach to the model reference control in LTV systems.
Highlights
Output regulation is one of the typical control strategies in the control systems synthesis and design
Output feedback trajectory tracking control problem is solved for autonomous underwater vehicles by combining the corresponding output feedback controllers and the finite-time convergent observer together [12]
Based on the solution of a type of generalized Sylvester matrix equations [29], a novel parametric form of a model reference tracking controller for linear time-varying (LTV) systems is proposed with a general solving procedure
Summary
Output regulation is one of the typical control strategies in the control systems synthesis and design. Based on the solution of a type of generalized Sylvester matrix equations [29], a novel parametric form of a model reference tracking controller for LTV systems is proposed with a general solving procedure. Based on the above discussion, the model reference control for linear time-varying systems can be stated as follows.
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