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New Prediction Approach For Stabilizing Time-Varying Systems Under Time-Varying Input Delay, Frederic Mazenc, Michael Malisoff
New Prediction Approach For Stabilizing Time-Varying Systems Under Time-Varying Input Delay, Frederic Mazenc, Michael Malisoff
Faculty Publications
We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems with pointwise time-varying input delays. Our method circumvents the problem of constructing and estimating distributed terms in the stabilizing control laws, and allows arbitrarily large input delay bounds. We illustrate our method using a pendulum dynamics.
Reduction Model Approach For Linear Time-Varying Systems With Input Delays Based On Extensions Of Floquet Theory, Frédéric Mazenc, Michael Malisoff
Reduction Model Approach For Linear Time-Varying Systems With Input Delays Based On Extensions Of Floquet Theory, Frédéric Mazenc, Michael Malisoff
Faculty Publications
We solve stabilization problems for linear time-varying systems under input delays. We show how changes of coordinates lead to systems with time invariant drifts, which are covered by the reduction model method and which lead to the problem of stabilizing a time-varying system without delay. For continuous time periodic systems, we can use Floquet theory to find the changes of coordinates. We also prove an analogue for discrete time systems, through a discrete time extension of Floquet theory.
Extension Of Razumikhin's Theorem For Time-Varying Systems With Delay, Frederic Mazenc, Michael Malisoff
Extension Of Razumikhin's Theorem For Time-Varying Systems With Delay, Frederic Mazenc, Michael Malisoff
Faculty Publications
We prove a new extension of Razumikhin's theorem that applies to time-varying nonlinear systems with time-varying delays, using a novel 'strictification' method for converting a nonstrict Lyapunov function into a strict Lyapunov function. We apply our method to a model from identification theory, to illustrate how our new result can allow broader classes of delays than earlier methods.
Stabilization In A Chemostat With Sampled And Delayed Measurements, Frédéric Mazenc, Jérome Harmand, Michael Malisoff
Stabilization In A Chemostat With Sampled And Delayed Measurements, Frédéric Mazenc, Jérome Harmand, Michael Malisoff
Faculty Publications
We study chemostat models with constant substrate input concentrations. We allow growth functions that are not necessarily monotone. The measurement is the substrate concentration, which is piecewise constant with a nonconstant delay, so only sampled observations are available. Under new conditions on the size of the delay and on the largest sampling interval, we solve the problem of asymptotically stabilizing a componentwise positive equilibrium point with the dilution rate as the control. We use a new Lyapunov approach.
New Control Design For Bounded Backstepping Under Input Delays, Frédéric Mazenc, Michael Malisoff
New Control Design For Bounded Backstepping Under Input Delays, Frédéric Mazenc, Michael Malisoff
Faculty Publications
We provide a new backstepping result for time-varying systems with input delays. The novelty of our work is in the bounds on the controls, and the facts that (i) one does not need to compute any Lie derivatives to apply our controls, (ii) the controls have no distributed terms, and (iii) we do not require any differentiability conditions on the available controls for the subsystems.