Abstract
This paper considers the stability problem for nonlinear quadratic systems with nested saturation input. The interesting treatment method proposed to nested saturation here is put into use a well-established linear differential control tool. And the new conclusions include the existing conclusion on this issue and have less conservatism than before. Simulation example illustrates the effectiveness of the established methodologies.
Highlights
In the past decades, there has been significant interest in the study of the quadratic systems due to such systems’ widely present from engineering systems to economic phenomena [1,2,3,4,5]
Based on the Lyapunov function and a particular presentation for the quadratic terms, the purpose of this paper is in a sense to be made precise of the sufficient conditions for local stabilization for the quadratic systems subject to nested saturation input in terms of LMIs
Through the new treatment of saturation nonlinearity given in Lemma 5, we divide three cases to estimate the RA for the quadratic system (4) subject to nested input saturation with conditional control design
Summary
There has been significant interest in the study of the quadratic systems due to such systems’ widely present from engineering systems to economic phenomena [1,2,3,4,5]. To some extent, such systems can accurately describe the interaction dynamics of various species, for example, in enzyme kinetics [6] or population models [7]. Numerous researches on the various control problems containing saturation nonlinearity have been conducted; for example, see [8, 9] and the references therein. We have two primary approaches to deal with saturation nonlinearity; one is to deal with the saturation nonlinearity as a local sector bound nonlinearity with different multipliers [10, 11]; the other [12, 13] is to conduct the saturation nonlinearity as a polytopic representation, which reduces less conservatism than the first one
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