Abstract
This paper proposes a novel system-augmentation approach to the delay-dependent reliable piecewise-affine $\mathscr {H}_{\infty }$ static output feedback control for nonlinear systems with time-varying delay and sensor faults in the piecewise-Markovian-Lyapunov-functional-based framework. The nonlinear plant is described by a continuous-time Takagi–Sugeno fuzzy-affine model with parametric uncertainties, and the sensor faults are characterized by a Markov process. Specifically, by applying a state-input augmentation technique, the original closed-loop system is first reformulated into a descriptor fuzzy-affine system. Based on a new piecewise-Markovian Lyapunov–Krasovskii functional, combined with a Wirtinger-based integral inequality, improved reciprocally convex inequality, and S -procedure, a novel bounded real lemma is then derived for the underlying closed-loop system. Furthermore, by taking advantage of the redundancy of descriptor system formulation, together with a linearization procedure, the piecewise-affine controller synthesis is carried out. It is shown that the desired piecewise-affine controller gains can be attained by solving a linear matrix inequality based optimization problem. Finally, simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach.
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