4 papers · 1 filter
Parameterization of Seed Functions for Equivalent Representations of Time-Varying Delay Systems
Sengiyumva Kisole, Jungbae Chun, Peter Seiler +1
Abel's classic transformation shows that any well-posed system with time-varying delay is equivalent to a parameter-varying system with fixed delay. The existence of such a paramet…
Lyapunov Functions can Exactly Quantify Rate Performance of Nonlinear Differential Equations
Declan S. Jagt, Matthew M. Peet
Pointwise-in-time stability notions for Ordinary Differential Equations (ODEs) provide quantitative metrics for system performance by establishing bounds on the rate of decay of th…
Bounding the Error of Value Functions in Sobolev Norm Yields Bounds on Suboptimality of Controller Performance
Morgan Jones, Matthew Peet
Optimal feedback controllers for nonlinear systems can be derived by solving the Hamilton-Jacobi-Bellman (HJB) equation. However, because the HJB equation is a nonlinear partial di…
Bounding the Settling Time of Finite-Time Stable Systems using Sum of Squares
Sengiyumva Kisole, Kunal Garg, Matthew Peet
Finite-time stability (FTS) of a differential equation guarantees that solutions reach a given equilibrium point in finite time, where the time of convergence depends on the initia…