A Separation Principle for Linear Switching Systems and Parametrization of All Stabilizing Controllers

被引:105
作者
Blanchini, Franco [1 ]
Miani, Stefano [2 ]
Mesquine, Fouad [3 ]
机构
[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy
[2] Univ Udine, UDipartimento Ingn Elettr Elettr & Informat, I-33100 Udine, Italy
[3] Cadi Ayad Univ, Dept Phys, Fac Sci, LAEPT, Marrakech 40000, Morocco
关键词
Lyapunov functions; separation principle; switching systems; Youla-Kucera parametrization; DISCRETE-TIME-SYSTEMS; LYAPUNOV FUNCTIONS; DESIGN; STABILIZABILITY; LIMITATIONS;
D O I
10.1109/TAC.2008.2010896
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we investigate the problem of designing a switching compensator for a plant switching amongst a (finite) family of given configurations (A(i), B-i, C-i). We assume that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the current configuration i. As a first result, we provide necessary and sufficient conditions for the existence of a switching compensator such that the closed-loop plant is stable under arbitrary switching. These conditions are based on a separation principle, precisely, the switching stabilizing control can be achieved by separately designing an observer and an estimated state (dynamic) compensator. These conditions are associated with (non-quadratic) Lyapunov functions. In the quadratic framework, similar conditions can be given in terms of LM Is which provide a switching controller which has the same order of the plant. As a second result, we furnish a characterization of all the stabilizing switching compensators for such switching plants. We show that, if the necessary and sufficient conditions are satisfied then, given any arbitrary family of compensators K-i(s), each one stabilizing the corresponding LTI plant (A(i), B-i, C-i) for fixed i, there exist suitable realizations for each of these compensators which assure stability under arbitrary switching.
引用
收藏
页码:279 / 292
页数:14
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