Work

Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS

Year: 2015

Type: conference-paper

Abstract: In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and their time derivatives by polynomials and express stability as optimization over polynomials. We use Sum-of-Squares and Positivstellensatz results to numerically search for a solution to the optimization over polynomials. We also show that our algorithm can be used to estimate the rate of decay of the solution to PDE in the L2norm. Finally, we validate the technique by applying our conditions to the 2D biological KISS PDE model of population growth and an additional example.

Source: IEEE Conference on Decision and Control (CDC)

DOI: 10.1109/cdc.2015.7402485

Authors: Evgeny Meyer, Matthew M. Peet

Institution: Arizona State University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CAREER: A New Computational Framework for Control of Complex Systems, Solving Large Sum-of-Squares Optimization Problems in Control by Exploiting the Parallel Structure of Polya's Algorithm