Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems

作者：Sadeghi Mokhtar Sha^*; Vafamand Navid; Babaei Mohammad Sadegh

来源：IET Science Measurement & Technology, 2014, 8(6): 537-545.

DOI：10.1049/iet-smt.2014.0038

• partial differential equations
• nonlinear differential equations
• hyperbolic equations
• fuzzy control
• control system synthesis
• nonlinear control systems
• distributed parameter systems
• Lyapunov methods
• linear matrix inequalities
• asymptotic stability
• nonquadratic exponential stabilisation
• nonlinear hyperbolic partial differential equation systems
• fuzzy controller design
• systematic approach
• TakagiaEuro" Sugeno fuzzy partial differential equation
• TS fuzzy-PDE system

In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi-Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study, non-quadratic Lyapunov function is utilised and some slack matrices are introduced to derive stability conditions in terms of linear matrix inequalities (LMIs). The proposed approach has three main features. First, stability conditions are not derived in the form of spatial differential LMI. Second, conservativeness of LMI conditions is reduced. Third, there is no restriction on the form of semi-linear hyperbolic PDE systems and therefore more semi-linear systems classes can be stabilised. Also, the proposed approach is more suitable for practical implementation compared with the recently published papers.

• 出版日期2014-11