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Control synthesis of reaction-diffusion systems with varying parameters and varying delays. (English) Zbl 1483.93178

Summary: In this paper, the analysis and state-feedback control synthesis for reaction-diffusion linear parameter-varying (LPV) systems with time delays and Robin boundary conditions are addressed. We explore the stability and \(\mathcal{L}_2\) gain performance for reaction-diffusion LPV systems using parameter-dependent Lyapunov functionals. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved via efficient convex optimisation solvers. A numerical example of automated blood pressure regulation via vasoactive drug infusion is explored to demonstrate the effectiveness of the proposed state-feedback control synthesis.

MSC:

93B50 Synthesis problems
93C20 Control/observation systems governed by partial differential equations
35K57 Reaction-diffusion equations
93B52 Feedback control
93C05 Linear systems in control theory
93C43 Delay control/observation systems
92C50 Medical applications (general)
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