Controllability of piecewise linear state-delay systems

Huiping Luo and JinRong Wang

Applied Mathematics and Computation, 2025, vol. 494, issue C

Abstract: In this paper, we study the controllability of piecewise linear state-delay systems (PLSDSs). To do this, we introduce a series of new functions and give the explicit representation of the solution. Then, the Gramian and the rank criteria for the controllability of PLSDSs are established by the piecewise delayed Gramian matrix. Further, all control functions driving the solution from an initial function to a desired final state are characterized by virtue of shifted Legendre polynomials. In addition, the controllability of PLSDSs constrained in an invariant subspace and weakly nonlinear piecewise systems are discussed as well, respectively. Numerical examples are provided to verify the effectiveness of theoretical results.

Keywords: Controllability; Piecewise system; State-delay; Control function; Shifted Legendre polynomial (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:494:y:2025:i:c:s0096300325000086

DOI: 10.1016/j.amc.2025.129281

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