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H ∞ mixed stabilization of nonlinear parameter‐varying systems
Author(s) -
Fu Rong,
Zeng Jianping,
Duan Zhisheng
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4304
Subject(s) - control theory (sociology) , nonlinear system , stability (learning theory) , mathematics , controller (irrigation) , attenuation , matrix (chemical analysis) , state (computer science) , mathematical optimization , computer science , control (management) , algorithm , physics , materials science , optics , quantum mechanics , artificial intelligence , machine learning , agronomy , composite material , biology
Summary This paper generalizes the existing finite‐time stability (FTS) analysis/synthesis research to nonlinear time‐varying systems in the nonlinear parameter‐varying (NPV) framework. Specifically, to guarantee both the transient and steady‐state performances for NPV systems with external disturbance and input constraints, concepts of mixed stability and mixed stability with H ∞ disturbance attenuation are proposed, together with the corresponding analysis and synthesis methods. Differently from the existing FTS‐related works, the mixed stability in this paper consists of properties of uniform exponential stability in addition to FTS. Existence conditions for an nonlinear time‐varying controller to render an NPV system mixed stable with H ∞ disturbance attenuation are given in terms of state‐and‐parameter–dependent linear matrix inequalities. The generalized S‐procedure is used to convexify the input constraints such that the resulting closed‐loop system satisfies the input constraints for any state starting from an admissible set. For the case that both parameters and state are subject to restricted regions, local synthesis results are also provided. All the conditions are in the form of state‐and‐parameter–dependent linear matrix inequalities, which can be efficiently solved by using sum‐of‐squares programming. A simulation example validates the effectiveness of the proposed approach.