Some results on simultaneous stabilization with multiple domains of stability |
| |
Affiliation: | 1. Department of Electrical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;1. College of Control Science and Engineering, Bohai University, Jinzhou 121013, Liaoning, China;2. College of Mathematical Science, Bohai University, Jinzhou, Liaoning 121013, China;3. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia;4. College of Information Science and Technology, Bohai University, Jinzhou 121007, Liaoning, China |
| |
Abstract: | In this paper, the problem of simultaneous stabilization in the case where each plant has a different domain of stability associated with it is studied. Specifically, it is supposed that one is given plants P0, P1,…, Pr together with domains of stability D0,…, Dr, and the objective is to find a common controller C such that the poles of the closed-loop transfer matrix H(Pi, C) are all inside the corresponding domain of stability Di, for i = 0,…, r. This formulation of the simultaneous stabilization problem generalizes earlier problem formulations wherein it was assumed that all the domains of stability were the same, and is believed to be a more realistic formulation of the problem of preserving system stability in the event of sensor or actuator failure. In the paper, necessary and sufficient conditions for the existence of a common controller are derived, in the case where one of the domains (say D0) is a subset of the rest. The case of two plants P0, P1 with D0 a subset of D1 is studied in great detail, and the following result is established: the two plants can be simultaneously stabilized in the above generalized sense if and only if they can be simultaneously stabilized with respect to the larger of the two regions. More precisely there exists a controller C such that the poles of H(Pi, C) lie inside Di for i = 0, 1 if and only if there exists a controller such that the poles of bothH(P0, C) and of H(P1, C) lie inside the larger region D1. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|