2018/12/12 by Sachin Shivakumar, Shivakumar, Sachin, Matthew M. Peet +1
Decision Sciences · Engineering · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1812.05081
openalex publication_date 2018/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose an LMI-based approach to analyze input-output properties of coupled linear PDE systems. This work expands on a newly developed state-space theory for coupled PDEs and extends the positive-real and bounded-real lemmas to infinite dimensional systems. We show that conditions for passivity and bounded L2 gain can be expressed as linear operator inequalities on RxL2. A method to convert these operator inequalities to LMIs by using parameterization of the operator variables is proposed. This method does not rely on discretization and as such, the properties obtained are prima facie provable. We use numerical examples to demonstrate that the bounds obtained are not conservative in any significant sense and that the bounds are computable on desktop computers for systems consisting of up to 20 coupled PDEs.