Abstract
This paper studies the problem of delay-dependent fixed-order memory piecewise-affine $\mathscr {H}_{\infty }$ output feedback control for a class of nonlinear systems with time-varying delay via a descriptor system approach. The nonlinear plant is expressed by a continuous-time Takagi-Sugeno (T-S) fuzzy-affine model. Specifically, by utilizing a descriptor model transformation, the original closed-loop system is firstly reformulated into a descriptor system. Based on a new type of Lyapunov-Krasovskii functional (LKF), combined with a Wirtinger-based integral inequality, reciprocally convex inequality and S-procedure, a novel $\mathscr {H}_{\infty }$ performance analysis criterion is then derived for the underlying closed-loop system. Furthermore, by explicitly taking advantage of the redundancy of descriptor system formulation, together with a linearization procedure, the piecewise-affine output feedback controller synthesis is carried out. It is shown that the desired fixed-order memory piecewise-affine controllers with different structures can be established in a unified framework. Finally, simulation studies are presented to show the effectiveness and less conservatism of the proposed approaches.
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