Abstract
We consider stabilization problem for reaction–diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a time-varying delay. To compensate the input delay, we construct an observer for the future value of the state. Using a time-varying observer gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The convergence conditions are obtained using a Lyapunov–Krasovskii functional, which leads to linear matrix inequalities (LMIs). We design output-feedback point controllers in the presence of input delays using the above observer. The boundary controller is constructed using the backstepping transformation, which leads to a target system containing the exponentially decaying estimation error. The in-domain point controller is designed and analysed using an improved Wirtinger-based inequality. We show that both controllers can guarantee the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer's estimation error.
Original language | English |
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Pages (from-to) | 224-233 |
Number of pages | 10 |
Journal | Automatica |
Volume | 96 |
DOIs | |
State | Published - Oct 2018 |
Keywords
- Boundary control
- Distributed parameter systems
- Input delay
- Networked control systems
- Point control
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Electrical and Electronic Engineering