## Abstract

This contribution focuses on the analysis and control of friction-dominated flow of gas in pipes. The pressure in the gas flow is governed by a partial differential equation that is a doubly nonlinear parabolic equation of p-Laplace type, where p = 3 2 p=\frac{3}{2}. Such equations exhibit positive solutions, finite speed of propagation and satisfy a maximum principle. The pressure is fixed on one end (upstream), and the flow is specified on the other end (downstream). These boundary conditions determine a unique steady equilibrium flow. We present a boundary feedback flow control scheme, that ensures local exponential stability of the equilibrium in an L 2 {L^{2}}-sense. The analysis is done both for the PDE system and an ODE system that is obtained by a suitable spatial semi-discretization. The proofs are based upon suitably chosen Lyapunov functions.

Original language | English (US) |
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Pages (from-to) | 1001-1010 |

Number of pages | 10 |

Journal | Automatisierungstechnik |

Volume | 68 |

Issue number | 12 |

DOIs | |

State | Published - Nov 18 2020 |

## Keywords

- Lyapunov function
- boundary feedback
- closed loop control
- exponential stability
- friction dominated model

## ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering