On Separable Quadratic Lyapunov Functions for Convex Design of Distributed Controllers

Abstract

We consider the problem of designing a stabilizing and optimal static controller with a pre-specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort to approximation approaches. In this paper, we characterize a class of convex restrictions of this problem that are based on designing a separable quadratic Lyapunov function for the closed-loop system. This approach generalizes previous results based on optimizing over diagonal Lyapunov functions, thus allowing for improved feasibility and performance. Moreover, we suggest a simple procedure to compute favourable structures for the Lyapunov function yielding high-performance distributed controllers. Numerical examples validate our results.

References in corpus (1)

• Robust Distributed Control Beyond Quadratic Invariance

Cited by in corpus (3)

• Data-based Receding Horizon Control of Linear Network Systems
• Sparsity Invariance for Convex Design of Distributed Controllers
• Closing the Gap to Quadratic Invariance: a Regret Minimization Approach to Optimal Distributed Control