On a conservative concept for output static stabilizability:analysis, consequences, and related problems

• Published in: International journal of control 2006-03, Vol.79 (3), p.185-206
• Main Authors: Najson, F., Speyer, J. L.
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Miscellaneous; Modelling and identification
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170500368883

This communication is concerned with the problem of stabilization, via output static feedback, of linear time-invariant finite-dimensional systems. A new output static stabilization concept is introduced: output static stabilization in the relaxed sense. This conservative stabilization concept is the result of imposing an additional condition to a set of necessary and sufficient conditions for output static stabilization. This paper is devoted to exhaustively study the introduced new stabilization concept: (I) It is shown that for a particular class of plants, the stabilization problem in the above sense can be cast as a convex programming problem. (II) A full characterization of the class of plants that are stabilizable in the above new sense is presented. Some of the important consequences of that study are as follows: (1) The identification of a class of plants stabilizable, via output static feedback, for which stabilizing feedback matrices can be (almost) expressed in analytic closed form. (2) It is shown that the introduced new conservative stabilization concept is much more significant that it appears; the general problem of output static stabilization can be transformed into the stabilization problem in this new conservative sense. (3) A relationship between output static stabilizability and the LQR problem is proved. (4) A novel generalization of the famous Lyapunov's theorem is presented. Convex necessary and sufficient conditions, for joint stabilization (of multiple plants) in the above sense and, for decentralized stabilization in the above sense, are also presented. Numerical examples illustrate some of the results.