113 citations · 211 across the 57 of their papers we have counts for
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A Converse Sum of Squares Lyapunov Function for Outer Approximation of Minimal Attractor Sets of Nonlinear Systems
Morgan Jones, Matthew M. Peet
Many dynamical systems described by nonlinear ODEs are unstable. Their associated solutions do not converge towards an equilibrium point, but rather converge towards some invariant…
Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets
Morgan Jones, Matthew M. Peet
In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equat…
Estimating the Region of Attraction Using Polynomial Optimization: a Converse Lyapunov Result
Hesameddin Mohammadi, Matthew M. Peet
In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which nece…
SOS Methods for Multi-Delay Systems: A Dual Form of Lyapanov-Krasovskii Functional
Matthew M. Peet
We present a dual form of Lyapunov-Krasovskii functional which allows the problem of controller synthesis of multi-delay systems to be formulated and solved in a convex manner. Fir…
Positive Forms and Stability of Linear Time-Delay Systems
Matthew M. Peet, Antonis Papachristodoulou, Sanjay Lall
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existe…
Stability and Control of Functional Differential Equations
Matthew M. Peet
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well…