113 citations · 211 across the 57 of their papers we have counts for
5 papers · 2 filters
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…
Dual Representations and -Optimal Control of Partial Differential Equations
Sachin Shivakumar, Amritam Das, Matthew Peet
We consider $\hinf$-optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While…
Extension of the Partial Integral Equation Representation to GPDE Input-Output Systems
Sachin Shivakumar, Amritam Das, Siep Weiland +1
It has been shown that the existence of a Partial Integral Equation (PIE) representation of a Partial Differential Equation (PDE) simplifies many numerical aspects of analysis, sim…
-Gain Analysis of Coupled Linear 2D PDEs using Linear PI Inequalities
Declan S. Jagt, Matthew M. Peet
In this paper, we present a new method for estimating the -gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using s…
Efficient Data Structures for Exploiting Sparsity and Structure in Representation of Polynomial Optimization Problems: Implementation in SOSTOOLS
Declan Jagt, Sachin Shivakumar, Peter Seiler +1
We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables are polynomial i…