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

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.

Inspec keywords: fuzzy control; nonlinear differential equations; partial differential equations; linear matrix inequalities; distributed parameter systems; hyperbolic equations; asymptotic stability; nonlinear control systems; Lyapunov methods; control system synthesis

Other keywords: TS fuzzy-PDE system; stability conditions; systematic approach; nonlinear distributed parameter system; LMI; nonquadratic Lyapunov function; nonquadratic exponential stabilisation; Takagi–Sugeno fuzzy partial differential equation; first order semilinear hyperbolic PDE; nonlinear hyperbolic partial differential equation systems; fuzzy controller design; linear matrix inequalities

Subjects: Differential equations (numerical analysis); Stability in control theory; Nonlinear control systems; Distributed parameter control systems; Fuzzy control; Linear algebra (numerical analysis); Nonlinear and functional equations (numerical analysis); Control system analysis and synthesis methods

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