2017/03/18 by Aditya Gahlawat, Gahlawat, Aditya, Giórgio Valmórbida +1
Engineering · #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1703.06371
We consider the stability analysis of a large class of linear 1-D PDEs with\npolynomial data. This class of PDEs contains, as examples, parabolic and\nhyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary\ncoupled PDEs. Our approach is Lyapunov based which allows us to reduce the\nstability problem to the verification of integral inequalities on the subspaces\nof Hilbert spaces. Then, using fundamental theorem of calculus and Green's\ntheorem, we construct a polynomial problem to verify the integral inequalities.\nConstraining the solution of the polynomial problem to belong to the set of\nsum-of-squares polynomials subject to affine constraints allows us to use\nsemi-definite programming to algorithmically construct Lyapunov certificates of\nstability for the systems under consideration. We also provide numerical\nresults of the application of the proposed method on different types of PDEs.\n