509 research outputs found
Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations
Lyapunov-like characterizations for non-uniform in time and uniform robust
global asymptotic stability of uncertain systems described by retarded
functional differential equations are provided
Decay Estimates for 1-D Parabolic PDEs with Boundary Disturbances
In this work decay estimates are derived for the solutions of 1-D linear
parabolic PDEs with disturbances at both boundaries and distributed
disturbances. The decay estimates are given in the L2 and H1 norms of the
solution and discontinuous disturbances are allowed. Although an eigenfunction
expansion for the solution is exploited for the proof of the decay estimates,
the estimates do not require knowledge of the eigenvalues and the
eigenfunctions of the corresponding Sturm-Liouville operator. Examples show
that the obtained results can be applied for the stability analysis of
parabolic PDEs with nonlocal terms.Comment: 35 pages, submitted for possible publication to ESAIM-COC
Nonlinear predictors for systems with bounded trajectories and delayed measurements
Novel nonlinear predictors are studied for nonlinear systems with delayed measurements without
assuming globally Lipschitz conditions or a known predictor map but requiring instead bounded state
trajectories. The delay is constant and known. These nonlinear predictors consists of a series of dynamic
filters that generate estimates of the state vector (and its maximum magnitude) at different delayed time
instants which differ from one another by a small fraction of the overall delay
- …