A probabilistic approach to the stability analysis of real-time control systems
| Authors: | Velasco Manel, Technical University of Catalonia, Spain
Martí Pau, Technical University of Catalonia, Spain
Villà Ricard, Technical University of Catalonia, Spain
Fuertes Josep M., Technical University of Catalonia, Spain
Ayza Jordi, Technical University of Catalonia, Spain
Monroig Miquel, Technical University of Catalonia, Spain |
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| Topic: | 3.1 Computers for Control |
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| Session: | Real-time Embedded Systems |
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| Keywords: | Real-time systems, Timing jitter, Random variables, Probabilistic models, Stability tests |
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Abstract
In real-time multitasking systems, feasible periodic tasks execute within theirperiods. However, the exact time at which each task executes vary dueto other task interferences. For control tasks,this produces irregular sampling and varying time delays, whichmay degrade system performance and bring the system to instability. Inthis paper we present stability conditions that allow us to evaluateif a closed-loop system designed to work at a nominal sampling period"hd" with a nominal time delay "td" will remain stable if the run-timesampling is not strictly periodic and time delays vary randomly. Inthe closed-loop system model, we consider the irregular sampling andthe varying time delays as random variables with knownexpectation. With this model, the system evolution can be seen as a sequenceof random state vectors generated by the system closed-loopmatrix. Then, we derive stability conditions for the system in termsof convergence of a sequence of random variables.
