On the Stabilization through Linear Output Feedback of a Class of Linear Hybrid Time-Varying Systems with Coupled Continuous/Discrete and Delayed Dynamics with Eventually Unbounded Delay
This research studies a class of linear, hybrid, time-varying, continuous time-systems with time-varying delayed dynamics and non-necessarily bounded, time-varying, time-differentiable delay. The considered class of systems also involves a contribution to the whole delayed dynamics with respect to t...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/56597 |
| Acceso en línea: | http://hdl.handle.net/10810/56597 |
| Access Level: | acceso abierto |
| Palabra clave: | hybrid dynamic systems time-varying delay sampled systems asymptotic stability asymptotic stabilization linear output feedback |
| Sumario: | This research studies a class of linear, hybrid, time-varying, continuous time-systems with time-varying delayed dynamics and non-necessarily bounded, time-varying, time-differentiable delay. The considered class of systems also involves a contribution to the whole delayed dynamics with respect to the last preceding sampled values of the solution according to a prefixed constant sampling period. Such systems are also subject to linear output-feedback time-varying control, which picks-up combined information on the output at the current time instant, the delayed one, and its discretized value at the preceding sampling instant. Closed-loop asymptotic stabilization is addressed through the analysis of two “ad hoc” Krasovskii–Lyapunov-type functional candidates, which involve quadratic forms of the state solution at the current time instant together with an integral-type contribution of the state solution along a time-varying previous time interval associated with the time-varying delay. An analytic method is proposed to synthesize the stabilizing output-feedback time-varying controller from the solution of an associated algebraic system, which has the objective of tracking prescribed suited reference closed-loop dynamics. If this is not possible—in the event that the mentioned algebraic system is not compatible—then a best approximation of such targeted closed-loop dynamics is made in an error-norm sense minimization. Sufficiency-type conditions for asymptotic stability of the closed-loop system are also derived based on the two mentioned Krasovskii–Lyapunov functional candidates, which involve evaluations of the contributions of the delay-free and delayed dynamics. |
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