University of Cambridge > > CUED Control Group Seminars > Chordal Sparsity, Decomposing SDPs and the Lyapunov Equation

Chordal Sparsity, Decomposing SDPs and the Lyapunov Equation

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Analysis questions in control theory are often formulated as Linear Matrix Inequalities and solved using convex optimisation algorithms. For large LMIs it is important to exploit structure and sparsity within the problem in order to solve the associated Semidefinite Programs efficiently. 

In this talk we discuss a method for decomposing SDPs based on chordal sparsity, and apply it to the problem of constructing Lyapunov functions for linear systems. By choosing Lyapunov functions with a chordal graphical structure we convert the semidefinite constraint in the problem into an equivalent set of smaller semidefinite constraints, thereby facilitating the solution of the problem. 

The approach has the potential to be applied to several other problems in control theory, such as stabilising controller synthesis, stability analysis of polynomial systems using Sum of Squares and the KYP lemma.

This talk is part of the CUED Control Group Seminars series.

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