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

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 us...

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Veröffentlicht in:International journal of robust and nonlinear control Jg. 31; H. 5; S. 1542 - 1563
Hauptverfasser: Reis, Gabriela L., Araújo, Rodrigo F., Torres, Leonardo A. B., Palhares, Reinaldo M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Bognor Regis Wiley Subscription Services, Inc 25.03.2021
Schlagworte:
Algebra
difference‐algebraic representation
Feedback control
gain‐scheduled state feedback
input saturation
Liapunov functions
Linear matrix inequalities
local stabilization
Nonlinear systems
Optimization
parameter‐dependent Lyapunov function
Representations
State feedback
ISSN:1049-8923, 1099-1239
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Zusammenfassung: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.
Bibliographie:Funding information
Conselho Nacional (CNPq) de Desenvolvimento Científico e Tecnológico, 307933/2018‐0; Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), PPM‐00053‐17
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.5362