Convex Stability Analysis of Nonlinear Singular Systems via Linear Matrix Inequalities

Arceo, Juan Carlos; Sánchez, Marcelino; Estrada-Manzo, Víctor; Bernal, Miguel

doi:10.1109/tac.2018.2854651

Cited by 36 publications

(14 citation statements)

References 36 publications

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“…In Section 4, it is possible to verify some numerical examples of discrete‐time nonlinear systems modeled in a DAR form. On the other hand, the existence of the inverse

Ω_{2}^{- 1} (x_{k}, δ_{k})

in (4) implies that it is considered in this paper difference‐algebraic systems that do not belong to the class of descriptor systems 50‐53 …”

Section: Problem Formulationmentioning

confidence: 99%

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Reis

Araujo

Tôrres

et al. 2020

Intl J Robust & Nonlinear

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Summary This paper addresses the local stabilization problem of nonlinear systems described by Difference‐Algebraic Representations (DAR). A novel set of sufficient Linear Matrix Inequalities (LMI) conditions are developed to design gain‐scheduled state feedback controllers. The proposed approach uses parameter‐dependent Lyapunov functions and new auxiliary decision variables aiming to obtain less conservative results. Two optimization problems are proposed to either obtain the largest estimated Domain‐of‐Attraction (DOA) or minimize the ℓ2‐gain from the energy‐bounded disturbance input to the performance output. Furthermore, this investigation considers control input saturation and system states constrained in a polyhedral region. Numerical examples are provided to illustrate the effectiveness of the proposed methodology, showing favorable comparisons with recently published similar approaches.

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“…In Section 4, it is possible to verify some numerical examples of discrete‐time nonlinear systems modeled in a DAR form. On the other hand, the existence of the inverse

Ω_{2}^{- 1} (x_{k}, δ_{k})

in (4) implies that it is considered in this paper difference‐algebraic systems that do not belong to the class of descriptor systems 50‐53 …”

Section: Problem Formulationmentioning

confidence: 99%

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Reis

Araujo

Tôrres

et al. 2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Then [5] and [6] have provided a Lyapunov-based analysis for linear DAE systems. In [7] the stability analysis of DAE systems has been performed by means of linear matrix inequalities, yielding necessary and sufficient conditions for the linear case and sufficient conditions for the nonlinear case. One of the first studies in the control of nonlinear DAE systems has been presented in [8], in which global stabilization and tracking problems for constrained mechanical systems have been solved by means of force feedback, while local results have been obtained by means of a linear controller.…”

Section: Introductionmentioning

confidence: 99%

A Globally Stable Algorithm for the Integration of High-Index Differential-Algebraic Systems

Franco

Scarciotti

Astolfi

2020

IEEE Trans. Automat. Contr.

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The problem of constraint stabilization and numerical integration for differential-algebraic systems is addressed using Lyapunov theory. It is observed that the application of stabilization methods which rely on a linear feedback mechanism to nonlinear systems may result in trajectories with finite escape time. To overcome this problem we propose a method based on a nonlinear stabilization mechanism which guarantees the global existence and convergence of the solutions. Discretization schemes, which preserve the properties of the method, are also presented. The results are illustrated by means of the numerical integration of a slider-crank mechanism.

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“…[36] and retaken in Refs. [37][38][39][40]. Nonetheless, in spite of the success of these paradigms, there is no literature review that allows tasting all the flavors offered by the vastness of convex approaches.…”

Section: Introductionmentioning

confidence: 99%

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

2019

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This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

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Convex Stability Analysis of Nonlinear Singular Systems via Linear Matrix Inequalities

Cited by 36 publications

References 36 publications

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

A Globally Stable Algorithm for the Integration of High-Index Differential-Algebraic Systems

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

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