2023/07/06 by Talha Mushtaq, Peter Seiler, Mushtaq, Talha +3
Engineering · #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2307.03330
openalex publication_date 2023/07/06 · openalex created_date 2023/07/11 · openalex updated_date 2026/07/28
Computing a stabilizing static output-feedback (SOF) controller is an NP-hard problem, in general. Yet, these controllers have amassed popularity in recent years because of their practical use in feedback control applications, such as fluid flow control and sensor/actuator selection. The inherent difficulty of synthesizing SOF controllers is rooted in solving a series of non-convex problems that make the solution computationally intractable. In this note, we show that SOF synthesis is a convex problem for the specific case of systems with a lossless (i.e., energy-conserving) nonlinearity. Our proposed method ensures asymptotic stability of an SOF controller by enforcing the lossless behavior of the nonlinearity using a quadratic constraint approach. In particular, we formulate a bilinear matrix inequality~(BMI) using the approach, then show that the resulting BMI can be recast as a linear matrix inequality (LMI). The resulting LMI is a convex problem whose feasible solution, if one exists, yields an asymptotically stabilizing SOF controller.