Abstract
In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.
Highlights
Descriptor systems are recognized as a powerful mathematical model able to describe the dynamic behavior as well as the interconnection properties of many practical plants [1,2]; referred to as singular systems, descriptor systems have known many applications in the fields related to electrical circuits, large-scale interconnected systems, electromechanical and constrained mechanical systems, economy, and biological systems
Based on the TS fuzzy models and the Lyapunov–Krasovskii functional, the admissibility analysis is firstly studied by combining the delay decomposition and the reciprocally convex combination approaches
A reliable static output feedback controller is designed such that the stability of the closed-loop system is ensured with accommodation of the negative effect caused by the sensors faults and noise
Summary
Descriptor systems are recognized as a powerful mathematical model able to describe the dynamic behavior as well as the interconnection properties of many practical plants [1,2]; referred to as singular systems, descriptor systems have known many applications in the fields related to electrical circuits, large-scale interconnected systems, electromechanical and constrained mechanical systems, economy, and biological systems. Up to now, the problem of mixed H∞ and passive reliable control and filtering for discrete-time descriptor systems with the simultaneous presence of randomly occurred non-linearities and sensor failures remains open and unsolved, despite their engineering importance in networked control systems This constitutes further motivation to carry out the present study. Except [32], the above-mentioned results are mainly focused on the case where the measured output vector is not influenced by the noise To handle this real case, the main objective of this paper is to pave the way for dealing with the problem of reliable fuzzy SOF controller design for TS fuzzy descriptor systems subject to time-varying delay, stochastic non-linearities and sensor failures. In what follows, hi denotes hi(θ), Xθ represents the the form ∑ri=1 convex combination ∑rj=1 hihj Xij
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