Robust stabilization of a class of polytopic linear time-varying continuous systems under point delays and saturating controls

2006 ◽  
Vol 181 (1) ◽  
pp. 73-83 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Linear Time ◽  
Robust Stabilization ◽  
Continuous Systems ◽  
Time Varying ◽  
Point Delays

scholarly journals On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-31 ◽  
Author(s):  
M. de la Sen ◽  
A. Ibeas
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
System Matrix ◽  
Almost Everywhere ◽  
Time Varying Systems ◽  
The Matrix ◽  
Delayed System ◽  
Point Delays

This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.

scholarly journals Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
M. de la Sen
Keyword(s):  
Dynamic System ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Linear Time ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Impulsive Controls ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations) which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that(q+1)polytopic parameterizations are considered for a system withqdelays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

Adaptive iterative learning control for unknown linear time-varying continuous systems

2019 ◽  
Vol 42 (5) ◽  
pp. 981-996
Author(s):  
Fateme Afsharnia ◽  
Ali Madady ◽  
Mohammad Bagher Menhaj
Keyword(s):  
Iterative Learning Control ◽  
Reference Model ◽  
Linear Time ◽  
Learning Control ◽  
Iterative Learning ◽  
Gronwall Lemma ◽  
Continuous Systems ◽  
Time Varying ◽  
Adaptive Iterative Learning Control ◽  
Time Varying Systems

This paper presents a novel model reference adaptive iterative learning control (ILC) for unknown continuous-time linear time-varying systems. The unknown time-varying parameters of the system are neither required to vary slowly nor to have known bounds. The system is not required to be minimum-phase, stable, controllable or observable. The input of the system is determined by a differentiator-free control law. The used reference model is time-invariant and first order and thus choosing its parameters is easily possible, even though, the system under control is high order and time variant. Almost all of the components of the system initial condition can be iteration variant. By introducing a novel kind of Lyapunov function the convergence of the proposed adaptive ILC (AILC) and achieving asymptotic tracking are proved. Also, by rigorous mathematical analysis and with the help of some mathematical key techniques such as Bellman-Gronwall lemma, it is shown that all signals and quantities in the closed-loop system are bounded in the sense of at least one norm. Finally, the effectiveness of the proposed method is verified by two simulation examples.

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