1. A. C. Antoulas, E. D. Sontag, and Y. Yamamoto. Controllability and Observability, pages 264-281. John Wiley & Sons, Inc., 2001. [WWW] [PDF] [doi:10.1002/047134608X.W1006] Keyword(s): reachability, controllability, observability, Lie algebra accessibility.



2. E.D. Sontag. Reachability, observability, and realization of a class of discrete-time nonlinear systems. In Encycl. of Systems and Control, pages 3288-3293. Pergamon Press, 1987. Keyword(s): observability.



3. E.D. Sontag. Comments on: ``Some results on pole-placement and reachability'' [Systems Control Lett. 6 (1986), no. 5, 325--328; MR0821927 (87c:93032)] by P. K. Sharma. Systems Control Lett., 8(1):79-83, 1986. [PDF] [doi:http://dx.doi.org/10.1016/0167-6911(86)90034-4] Keyword(s): systems over rings, parametric classes of systems. Abstract:

   We present various comments on a question about systems over rings posed in a recent note by Sharma, proving that a ring R is pole-assignable if and only if, for every reachable system (F,G), G contains a rank-one summand of the state space. We also provide a generalization to deal with dynamic feedback.




4. E.D. Sontag. On finitary linear systems. Kybernetika (Prague), 15(5):349-358, 1979. [PDF] Keyword(s): systems over rings, parametric classes of systems. Abstract:

   An abstract operator approach is introduced, permitting a unified study of discrete- and continuous-time linear control systems. As an application, an algorithm is given for deciding if a linear system can be built from any fixed set of linear components. Finally, a criterion is given for reachability of the abstract systems introduced, giving thus a unified proof of known reachability results for discrete-time, continuous-time, and delay-differential systems.




5. E.D. Sontag and Y. Rouchaleau. On discrete-time polynomial systems. Nonlinear Anal., 1(1):55-64, 1976. [PDF] Keyword(s): identifiability, observability, polynomial systems, realization theory, discrete-time. Abstract:

   Considered here are a type of discrete-time systems which have algebraic constraints on their state set and for which the state transitions are given by (arbitrary) polynomial functions of the inputs and state variables. The paper studies reachability in bounded time, the problem of deciding whether two systems have the same external behavior by applying finitely many inputs, the fact that finitely many inputs (which can be chosen quite arbitrarily) are sufficient to separate those states of a system which are distinguishable, and introduces the subject of realization theory for this class of systems.

1. A.C.B de Olivera, M. Siami, and E.D. Sontag. Bilinear dynamical networks under malicious attack: an efficient edge protection method. In Proc. 2021 Automatic Control Conference, pages 1210-1216, 2021. [PDF] Keyword(s): Bilinear systems, adversarial attacks, robustness measures, supermodular optimization. Abstract:

   In large-scale networks, agents and links are often vulnerable to attacks. This paper focuses on continuous-time bilinear networks, where additive disturbances model attacks or uncertainties on agents/states (node disturbances), and multiplicative disturbances model attacks or uncertainties on couplings between agents/states (link disturbances). It investigates network robustness notion in terms of the underlying digraph of the network, and structure of exogenous uncertainties and attacks. Specifically, it defines a robustness measure using the $\mathcal H_2$-norm of the network and calculates it in terms of the reachability Gramian of the bilinear system. The main result is that under certain conditions, the measure is supermodular over the set of all possible attacked links. The supermodular property facilitates the efficient solution finding of the optimization problem. Examples illustrate how different structures can make the system more or less vulnerable to malicious attacks on links.

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