Abstract
We study the concept of stabilization with internal loop for infinite‐dimensional discrete time‐varying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the controller with internal loop overcomes the awkwardness brought by the extra invertibility condition in the parametrization of the conventional controllers. We also prove that the strong stabilization problem can be completely solved in the closed‐loop system with internal loop. Thus the advantage of the controller with internal loop is addressed in the framework of nest algebra.
Highlights
The closed-loop system whose stability is achieved by the controller with internal loop has attracted the attention of many authors in recent years see 1–5
Suppose I − C22 is invertible in L, P can be stabilized by a canonical controller with internal loop if and only if P is stabilizable in the framework of standard feedback system
The closed-loop system whose stability is achieved by the controller with internal loop is studied in the framework of nest algebra
Summary
The closed-loop system whose stability is achieved by the controller with internal loop has attracted the attention of many authors in recent years see 1–5. When they extended the theory of dynamic stabilization to regular linear systems a subclass of the well-posed linear systems , it was shown in Example 6.5 of 1 that even the standard observer-based controller is not a well-posed linear system as needed, correspondingly, its transfer function is not wellposed To overcome this difficulty, a new type of controller, the so-called stabilizing controller with internal loop, was introduced. We study the concept of stabilization with internal loop for the linear time-varying system under the framework of nest algebra.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
