On strong structural controllability and observability of linear time-varying systems: a constructive method

Abstract

In this paper, we consider the controllability and observability of generalized linear time-varying (LTV) systems whose coefficients are not exactly known. All that is known about these systems is the placement of non-zero entries in their coefficient matrices (A,B). We provide the characterizations in order to judge whether the placements can guarantee the controllability/observability of such LTV systems, regardless of the exact value of each non-zero coefficient. We also present a direct and efficient algorithm with an associated time cost of O(n+m+v) to verify the conditions of our characterizations, where n and m denote the number of columns of A and B, respectively, and v is number of non-zero entries in (A,B).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61233004, 61590924, 61521063).

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Correspondence to Shaoyuan Li.

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Li, S., Mu, J. & Wang, Y. On strong structural controllability and observability of linear time-varying systems: a constructive method. Sci. China Inf. Sci. 62, 12205 (2019). https://doi.org/10.1007/s11432-017-9311-x

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Keywords

  • linear time-varying (LTV) systems
  • strong structural properties
  • controllability
  • observability
  • duality