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Stabilization And Robustness Analysis For Time-Varying Systems With Time-Varying Delays Using A Sequential Subpredictors Approach, Frédéric Mazenc, Michael Malisoff
Stabilization And Robustness Analysis For Time-Varying Systems With Time-Varying Delays Using A Sequential Subpredictors Approach, Frédéric Mazenc, Michael Malisoff
Faculty Publications
We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems. Our method circumvents the problem of constructing and estimating distributed terms in the control laws, and allows arbitrarily large input delay bounds, pointwise time-varying input delays, and uncertainties. Instead of using distributed terms, our approach to handling longer delays is to increase the number of predictors. We obtain explicit formulas to find lower bounds for the number of required predictors. The formulas involve bounds on the delays and on the derivatives of the delays. We illustrate our method in three examples.
Stabilization Of Nonlinear Time-Varying Systems Through A New Prediction Based Approach, Frederic Mazenc, Michael Malisoff
Stabilization Of Nonlinear Time-Varying Systems Through A New Prediction Based Approach, Frederic Mazenc, Michael Malisoff
Faculty Publications
We propose a prediction based stabilization approach for a general class of nonlinear time-varying systems with pointwise delay in the input. It is based on a recent new prediction strategy, which makes it possible to circumvent the problem of constructing and estimating distributed terms in the expression for the stabilizing control laws. Our result applies in cases where other recent results do not.
Extensions Of Razumikhin's Theorem And Lyapunov–Krasovskii Functional Constructions For Time-Varying Systems With Delay, Frédéric Mazenc, Michael Malisoff
Extensions Of Razumikhin's Theorem And Lyapunov–Krasovskii Functional Constructions For Time-Varying Systems With Delay, Frédéric Mazenc, Michael Malisoff
Faculty Publications
We prove extensions of Razumikhin's theorem for time-varying continuous and discrete time nonlinear systems. Our results include a novel ‘strictification’ technique for converting a nonstrict Lyapunov function into a strict one. We also provide new constructions of Lyapunov–Krasovskii functionals that can be used to prove robustness to perturbations. Our examples include a key model from identification theory, and they show how our method can sometimes allow broader classes of delays than the results in the literature.
Stabilization In A Chemostat With Sampled And Delayed Measurements And Uncertain Growth Functions, Frédéric Mazenc, Jérome Harmand, Michael Malisoff
Stabilization In A Chemostat With Sampled And Delayed Measurements And Uncertain Growth Functions, Frédéric Mazenc, Jérome Harmand, Michael Malisoff
Faculty Publications
We provide a new control design for chemostats, under constant substrate input concentrations, using piecewise constant delayed measurements of the substrate concentration. Our growth functions can be uncertain and are not necessarily monotone. The dilution rate is the control. We use a new Lyapunov approach to derive conditions on the largest sampling interval and on the delay length to ensure asymptotic stabilization properties of a componentwise positive equilibrium point.
Stability And Robustness Analysis For Human Pointing Motions With Acceleration Under Feedback Delays, Paul Varnell, Michael Malisoff, Fumin Zhang
Stability And Robustness Analysis For Human Pointing Motions With Acceleration Under Feedback Delays, Paul Varnell, Michael Malisoff, Fumin Zhang
Faculty Publications
Pointer acceleration is often used in computer mice and other interfaces to increase the range and speed of pointing motions without sacrificing precision during slow movements. However, the effects of pointer acceleration are not yet well understood. We use a system perspective and feedback control to analyze the effects of pointer acceleration. We use a new pointer acceleration model connected in feedback with the vector integration to endpoint model for pointing motions. When there are no feedback delays, we prove global asymptotic stability of the closed loop system for a general class of acceleration profiles. We also prove robustness under …
Stability And Control Design For Time-Varying Systems With Time-Varying Delays Using A Trajectory-Based Approach, Frederic Mazenc, Michael Malisoff, Silviu Iulian Niculescu
Stability And Control Design For Time-Varying Systems With Time-Varying Delays Using A Trajectory-Based Approach, Frederic Mazenc, Michael Malisoff, Silviu Iulian Niculescu
Faculty Publications
A recent work by Mazenc and Malisoff provides a trajectory-based approach for proving stability of time-varying systems with time-varying delays. Here, we provide several significant applications of their approach. In two results, we use a Lyapunov function for a corresponding undelayed system to provide a new method for proving stability of linear continuous-time time-varying systems with bounded time-varying delays. We allow uncertainties in the coefficient matrices of the systems. Our main results use upper bounds on an integral average involving the delay. The results establish input-to-state stability with respect to disturbances. We also provide a novel reduction model approach that …