113 citations · 211 across the 57 of their papers we have counts for
59 papers
Constructive Representation of Functions in -Dimensional Sobolev Space
Declan S. Jagt, Matthew M. Peet
A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an -dimensional hyperrectangle. In particular, it is shown that these funct…
Integral Quadratic Constraints with Infinite-Dimensional Channels
Aleksandr Talitckii, Peter Seiler, Matthew M. Peet
Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Per…
Efficient Convex Algorithms for Universal Kernel Learning
Aleksandr Talitckii, Brendon K. Colbert, Matthew M. Peet
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of k…
A PIE Representation of Scalar Quadratic PDEs and Global Stability Analysis Using SDP
Declan Jagt, Peter Seiler, Matthew Peet
It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial der…
Representation of linear PDEs with spatial integral terms as Partial Integral Equations
Sachin Shivakumar, Amritam Das, Matthew Peet
In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial int…
Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems
Morgan Jones, Matthew M. Peet
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to se…