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Randomized system trajectories

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Abstract

The notion of system trajectory of a time-varying input-output, dynamical system is reviewed. By introducing a probability measure on a class of such systems a stochastic system, the randomized system, is defined. The randomized system has a trajectory induced by the trajectories of the original systems. A theorem is proved giving fairly general conditions under which the randomized system trajectory is generated by a strongly continuous semigroup of bounded linear operators in a Banach space. An example is presented for a system represented by a quadratic integral operator.

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Authors and Affiliations

  1. Aerospace Engineering Department and Computer, Information, and Control Engineering Program, The University of Michigan, 48109, Ann Arbor, MI, USA

    William L. Root

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  1. William L. Root
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Additional information

Communicated by A. V. Balakrishnan

Research supported in part by National Science Foundation under Grant No. ECS-8005960.

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Root, W.L. Randomized system trajectories. Appl Math Optim 8, 293–307 (1982). https://doi.org/10.1007/BF01447765

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  • DOI: https://doi.org/10.1007/BF01447765

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