113 citations · 211 across the 57 of their papers we have counts for
7 papers · 1 filter
Representation and Stability Analysis of PDE-ODE Coupled Systems
Amritam Das, Sachin Shivakumar, Siep Weiland +1
In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial d…
A Partial Integral Equation (PIE) Representation of Coupled Linear PDEs and Scalable Stability Analysis using LMIs
Matthew M. Peet
We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability ana…
Extensions of the Dynamic Programming Framework: Battery Scheduling, Demand Charges, and Renewable Integration
Morgan Jones, Matthew M. Peet
We consider a general class of Dynamic Programming (DP) problems with non-separable objective functions. We show that for any problem in this class, there exists an augmented-state…
Using SOS for Optimal Semialgebraic Representation of Sets: Finding Minimal Representations of Limit Cycles, Chaotic Attractors and Unions
Morgan Jones, Matthew M. Peet
In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of di…
A Convex Solution of the -Optimal Controller Synthesis Problem for Multi-Delay Systems
Matthew M. Peet
Optimal controller synthesis is a bilinear problem and hence difficult to solve in a computationally efficient manner. We are able to resolve this bilinearity for systems with dela…
A New State-Space Representation of Lyapunov Stability for Coupled PDEs and Scalable Stability Analysis in the SOS Framework - with Lemma Proofs
Matthew M. Peet
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes…