Global stabilization of a certain class of nonlinear systems

Seibert, Peter; Suárez, Rodolfo

doi:10.1016/0167-6911(91)90024-9

Cited by 20 publications

(12 citation statements)

References 15 publications

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“…Similarly for anyx ∈ 3V 2 (c 1 ), we have x ∈ 3V 1 (c 1 ) and this implies that C x 4 . Therefore, for anyx ∈ 3V 2 (c 1 ), both saturations are inactive.…”

Section: Wang Et Almentioning

confidence: 91%

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Stabilization of nonlinear sandwich systems via state feedback—Discrete‐time systems

Wang

Stoorvogel

Saberi

et al. 2010

Intl J Robust & Nonlinear

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SUMMARYA recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156-2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched between linear systems. We focus first on single-layer sandwich systems, which consist of a single saturation sandwiched between two linear systems. For such systems, we present necessary and sufficient conditions for semi-global and global stabilization problems by state feedback, and develop design methodologies to achieve the prescribed stabilization. We extend the results to single-layer sandwich systems subject to additional actuator saturation. Finally, we discuss further extension to general multi-layer sandwich systems with an arbitrary number of saturations sandwiched between linear systems, both with and without actuator saturation. The design methodologies can be viewed as extensions of classical low-gain design methodologies developed during the 1990s in the context of stabilizing linear systems subject to actuator saturation.

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“…Similarly for anyx ∈ 3V 2 (c 1 ), we have x ∈ 3V 1 (c 1 ) and this implies that C x 4 . Therefore, for anyx ∈ 3V 2 (c 1 ), both saturations are inactive.…”

Section: Wang Et Almentioning

confidence: 91%

“…Consider the interconnection of the two systems given by (3) and (4). Both the semi-global and global stabilization problems, as formulated in Problems 1 and 2, are solvable if and only if, 1.…”

Section: Theoremmentioning

confidence: 99%

Stabilization of nonlinear sandwich systems via state feedback—Discrete‐time systems

Wang

Stoorvogel

Saberi

et al. 2010

Intl J Robust & Nonlinear

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“…Sandwiched systems such as depicted in Figures 1 and 2 are a special case of so-called cascade systems which are linear systems whose output affects a nonlinear system. This research was initiated in [8] but has also been studied in for instance [10], [11]. Note that in our case the nonlinear system has a very special structure of an interconnection of a static nonlinearity with a linear system.…”

Section: Introductionmentioning

confidence: 97%

Stabilization of a class of sandwich nonlinear systems via state feedback

Wang

Stoorvogel

Saberi

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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“…The research on such cascaded systems was initiated in [4] but has also been studied in for instance [7], [8]. Note that in our case the nonlinear system has a very special structure of an interconnection of a static nonlinearity with a linear system.…”

Section: Introductionmentioning

confidence: 98%