, On the other hand, under the same setting, characterizations for structural controllability in graphtheoretical terms has recently been provided in [47]; a sufficient condition for s-structural controllability, for structural (resp. s-structural) ISO, given in Chapters 2, 3, 4 are also reliant on this requirement, vol.3

, Under LTV setting with fixed graphs and dependent parameters, a graphical characterization for structural ISO can be obtained by combining the results in Chapter 3 (see Props. 12 and 13) and that in, vol.47

, However, the following problems remain open. (i) under LTI setting with dependent free parameters and arbitrary input, output and feedthrough matrices, a graphical characterization for structural ISO

, LTV setting with at least one dependent parameter, accounting for arbitrary input, output and feedthrough matrices and time-varying topology, purely algebraic characterizations and graph-theoretical characterizations for structural ISO

, et al operates under the assumption that the free parameters are free to take any value over the field of real (or complex) numbers. However, there exist setups where a free parameter is allowed to take only a finite set of values, i.e., over a finite field. Characterizations of structural controllability (and observability) over finite fields have been studied in, vol.78

. However, The main difficulty seems to be the following: graphical characterization for structural ISO is reliant on an algebraic characterization, namely PBH-like test (see Prop. 1 in [22]). Since finite fields are not algebraically closed, i.e., not every polynomial with coefficients from a finite field will have a root in that field, the best of our knowledge, similar characterizations for structural ISO are not yet available

S. Amin, A. A. Cárdenas, and S. Sastry, Safe and secure networked control systems under denial-of-service attacks, International Workshop on Hybrid Systems: Computation and Control, pp.31-45, 2009.

D. O. Brian, H. Anderson, and . Hong, Structural controllability and matrix nets, In: International Journal of Control, vol.35, p.103, 1982.

A. Esna-ashari, A. Y. Kibangou, and F. Garin, Distributed input and state estimation for linear discrete-time systems, pp.782-787, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00725518

S. Assadi, Complexity of the Minimum Input Selection Problem for Structural Controllability, In: IFAC-PapersOnLine, vol.48, p.101, 2015.

T. Boukhobza, F. Hamelin, and S. Martinez-martinez, State and input observability for structured linear systems: A graph-theoretic approach, In: Automatica, vol.43, pp.1204-1210, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00152192

S. Alvaro-a-cardenas, S. Amin, and . Sastry, Research Challenges for the Security of Control Systems, Proc. of the 3rd Conf. on Hot Topics in Security, p.105, 2008.

. Alvaro-a-cárdenas, Attacks against process control systems: risk assessment, detection, and response, Proceedings of the 6th ACM symposium on information, p.105, 2011.

A. Chapman and M. Mesbahi, On strong structural controllability of networked systems: a constrained matching approach, 2013.

D. C. Washington and U. , , vol.56, p.59, 2013.

K. Roshan-a-chavan and H. Fitch, Recursive input reconstruction with a delay, American Control Conference (ACC), pp.628-633, 2014.

Y. Chen, S. Kar, and . Moura, Distributed Estimation Under Sensor Attacks, p.105, 2017.

C. Commault and J. Dion, The single-input minimal controllability problem for structured systems, Systems & Control Letters, vol.80, p.101, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01154379

C. Commault, J. Dion, and D. Trinh, Observability preservation under sensor failure, IEEE Transactions on Automatic Control, vol.53, p.56, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00320200

C. Commault, J. Dion, and J. W. Van-der-woude, Characterization of generic properties of linear structured systems for efficient computations, In: Kybernetika, vol.38, pp.503-520, 2002.

C. Commault, J. Van-der-woude, and T. Boukhobza, On the fixed controllable subspace in linear structured systems, Systems & Control Letters, vol.102, p.102, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01480697

J. Conti, The day the samba stopped, In: Engineering & Technology, vol.5, pp.46-47, 2010.

J. Corfmat and . Morse, Structurally controllable and structurally canonical systems, IEEE Transactions on Automatic Control, vol.21, p.103, 1976.

M. Darouach, M. Onana, and . Zasadzinski, State estimation of stochastic singular linear systems: convergence and stability, In: International journal of systems science, vol.24, pp.1001-1008, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00143909

M. Darouach, M. Zasadzinski, and D. Mehdi, State estimation of stochastic singular linear systems, In: International Journal of Systems Science, vol.24, pp.345-354, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00143947

G. De-nicolao, G. Sparacino, and C. Cobelli, Nonparametric input estimation in physiological systems: problems, methods, and case studies, In: Automatica, vol.33, p.48, 1997.

J. Dion, C. Commault, and J. Van-der-woude, Generic properties and control of linear structured systems: a survey, In: Automatica, vol.39, pp.1125-1144, 2003.

V. S. Dolk, Event-Triggered Control Systems Under Denial-of-Service Attacks, IEEE Transactions on Control of Network Systems, vol.4, pp.93-105, 2017.

F. Garin, Structural Delay-1 Input-and-State Observability, pp.2324-2329, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01592199

F. Garin, S. Gracy, and A. Kibangou, Unbiased Filtering for State and Unknown Input with Delay, Proc. 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys). IFAC. Gronigen, p.83, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01850957

S. Gillijns and B. D. Moor, Unbiased minimum-variance input and state estimation for linear discrete-time systems, In: Automatica, vol.43, pp.3-5, 2007.

S. Gillijns and B. D. Moor, Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough, In: Automatica, vol.43, pp.934-937, 2007.

C. Godsil and G. Royle, Algebraic graph theory, Graduate Texts in Mathematics, vol.207, p.18, 2001.

M. Charles-golumbic, T. Hirst, and M. Lewenstein, Uniquely restricted matchings, In: Algorithmica 31, vol.2, p.41, 2001.

S. Gracy, F. Garin, and A. Kibangou, Structural and Strongly Structural Input and State Observability of Linear Network Systems, IEEE Transactions on Control of Network Systems, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01663175

S. Gracy, F. Garin, and A. Y. Kibangou, Input and State Observability of Network Systems with time-varying toplogy, IEEE Transactions on Control of Network Systems, p.66, 2018.

Y. Guan, Structural controllability of higher-order multi-agent systems under absolute and relative protocols, Control Conference (CCC), pp.6832-6837, 2013.

C. Hartung, G. Reißig, and F. Svaricek, Characterization of strong structural controllability of uncertain linear time-varying discrete-time systems, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), p.33, 2012.

D. Hershkowitz and H. Schneider, Ranks of zero patterns and sign patterns, In: Linear and Multilinear Algebra, vol.34, pp.3-19, 1993.

P. Holme, Network reachability of real-world contact sequences, In: Physical Review E, vol.71, p.46119, 2005.

E. John, R. Hopcroft, and . Karp, A n 5/2 algorithm for maximum matchings in bipartite, 12th Annual Symposium on Switching and Automata Theory, p.57, 1971.

C. Hsieh, Robust two-stage Kalman filters for systems with unknown inputs, IEEE Transactions on Automatic Control, vol.45, pp.2374-2378, 2000.

J. Christian-jarczyk, F. Svaricek, and B. Alt, Determination of the dimensions of strong structural controllable subspaces, IFAC Proceedings Volumes, vol.43, p.102, 2010.

J. Christian-jarczyk, F. Svaricek, and B. Alt, Strong structural controllability of linear systems revisited, Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference, pp.1213-1218, 2011.

M. Ji and M. Egerstedt, Observability and estimation in distributed sensor networks, 46th IEEE, pp.4221-4226, 2007.

J. Jia, A Sufficient Condition for Colored Strong Structural Controllability of Networks, Proc. 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys). IFAC. Gronigen, p.103, 2018.

Y. Alain, C. Kibangou, and . Commault, Observability in connected strongly regular graphs and distance regular graphs, IEEE transactions on control of network systems, vol.1, pp.360-369, 2014.

A. Y. Kibangou, F. Garin, and S. Gracy, Input and state observability of network systems with a single unknown input, Proc. 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys). IFAC, vol.107, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01368906

S. Kirtikar, L-delay input and initial-state reconstruction for discrete-time linear systems, In: Circuits, Systems, and Signal Processing, vol.30, pp.233-262, 2011.

. William-s-levine, The Control Handbook, p.50, 1996.

T. Li and J. Zhang, Consensus conditions of multi-agent systems with timevarying topologies and stochastic communication noises, IEEE Transactions on Automatic Control, vol.55, pp.2043-2057, 2010.

G. Liang, The 2015 ukraine blackout: Implications for false data injection attacks, IEEE Transactions on Power Systems, vol.32, pp.3317-3318, 2017.

C. Lin, Structural controllability, IEEE Transactions on Automatic Control, vol.19, pp.102-104, 1974.

F. Liu and . Stephen-morse, Structural Controllability of Linear Time-invariant Systems, p.103, 2017.

X. Liu, H. Lin, and B. Chen, Structural controllability of switched linear systems, Automatica 49, vol.12, p.66, 2013.

Y. Liu, P. Ning, and M. Reiter, False data injection attacks against state estimation in electric power grids, In: ACM Transactions on Information and System Security, vol.14, p.13, 2011.

J. L. Massey and . Michael-k-sain, Inverses of linear sequential circuits, In: IEEE Transactions on Computers, vol.100, pp.330-337, 1968.

H. Mayeda and T. Yamada, Strong structural controllability, In: SIAM Journal on Control and Optimization, vol.17, pp.123-138, 1979.

A. Mitra and S. Sundaram, Distributed observers for LTI systems, p.105, 2016.

A. Mitra and S. Sundaram, Resilient Distributed State Estimation for LTI Systems, p.105, 2018.

A. Mitra and S. Sundaram, Secure Distributed State Estimation of an LTI System over Time-Varying Networks and Analog Erasure Channels, p.105, 2018.

Y. Mo, R. Chabukswar, and B. Sinopoli, Detecting integrity attacks on SCADA systems, IEEE Transactions on Control Systems Technology, vol.22, pp.1396-1407, 2014.

K. Murota, Matrices and matroids for systems analysis, vol.20, 2009.

. Neave-o'clery, Observability and coarse graining of consensus dynamics through the external equitable partition, In: Physical Review E, vol.88, p.42805, 2013.

A. Olshevsky, Minimal controllability problems, IEEE Transactions on Control of Network Systems, vol.1, p.101, 2014.

D. Harish-j-palathandalam-madapusi and . Bernstein, Unbiased minimum-variance filtering for input reconstruction, pp.5712-5717, 2007.

G. Parlangeli and G. Notarstefano, On the reachability and observability of path and cycle graphs, IEEE Transactions on Automatic Control, vol.57, issue.3, pp.743-748, 2012.

A. Partovi, H. Lin, and Z. Ji, Structural controllability of high order dynamic multi-agent systems, Robotics Automation and Mechatronics (RAM), 2010 IEEE Conference on. IEEE. 2010, pp.327-332

F. Pasqualetti, F. Dörfler, and F. Bullo, Attack detection and identification in cyber-physical systems, IEEE Transactions on Automatic Control, vol.58, pp.2715-2729, 2013.

F. Pasqualetti, F. Dorfler, and F. Bullo, Control-theoretic methods for cyberphysical security: Geometric principles for optimal cross-layer resilient control systems, IEEE Control Systems, vol.35, pp.110-127, 2015.

F. Pasqualetti, F. Dörfler, and F. Bullo, Cyber-physical attacks in power networks: Models, fundamental limitations and monitor design, Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference, pp.2195-2201, 2011.

J. Ron, P. M. Patton, R. Frank, and . Clarke, Fault diagnosis in dynamic systems: theory and application, p.48, 1989.

L. D. Penso, D. Rautenbach, and U. Souza, Graphs in which some and every maximum matching is uniquely restricted, In: Journal of Graph Theory, p.33, 2015.

S. Pequito, S. Kar, and . Aguiar, A framework for structural input/output and control configuration selection in large-scale systems, IEEE Transactions on Automatic Control, vol.61, p.101, 2016.

S. Pequito, S. Kar, and . Aguiar, Minimum cost input/output design for large-scale linear structural systems, Automatica, vol.68, p.101, 2016.

S. Poljak, On the gap between the structural controllability of time-varying and time-invariant systems, IEEE Transactions on Automatic Control, vol.37, pp.1961-1965, 1992.

S. Poljak, On the generic dimension of controllable subspaces, In: IEEE Transactions on Automatic Control, vol.35, pp.367-369, 1990.

G. Reissig, C. Hartung, and F. Svaricek, Strong structural controllability and observability of linear time-varying systems, IEEE Transactions on Automatic Control, vol.59, pp.3087-3092, 2014.

. Craig-g-rieger, M. David-i-gertman, and . Mcqueen, Resilient control systems: Next generation design research, Human System Interactions, 2009. HSI'09. 2nd Conference on, p.105, 2009.

W. Robert, . Shields, and . Boyd-pearson, Structural controllability of multi-input linear systems, vol.104, p.22, 1975.

J. Slay and M. Miller, Lessons learned from the Maroochy water breach, International Conference on Critical Infrastructure Protection, pp.73-82, 2007.

S. Roy and . Smith, A decoupled feedback structure for covertly appropriating networked control systems, IFAC Proceedings Volumes, vol.44, pp.90-95, 2011.

S. Sundaram, Fault-tolerant and secure control systems, Lecture Notes, vol.84, p.12, 2018.

S. Sundaram, . Christoforos, and . Hadjicostis, Delayed observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, vol.52, pp.334-339, 2007.

S. Sundaram, . Christoforos, and . Hadjicostis, Structural controllability and observability of linear systems over finite fields with applications to multi-agent systems, IEEE Transactions on Automatic Control, vol.58, p.103, 2013.

S. Sundaram, G. Shai-revzen, and . Pappas, A control-theoretic approach to disseminating values and overcoming malicious links in wireless networks, In: Automatica, vol.48, pp.2894-2901, 2012.

D. Swart, Input and State Estimation for Linear Ystems with Sparse Unknown Input, 2018.

A. Teixeira, H. Sandberg, and . Johansson, Networked control systems under cyber attacks with applications to power networks, Proceedings of the 2010

A. Control-conference, M. D. Baltimore, and U. , , p.48, 2010.

A. Teixeira, A secure control framework for resource-limited adversaries, Automatica, vol.51, pp.135-148, 2015.

M. Trefois and J. Delvenne, Zero forcing number, constrained matchings and strong structural controllability, Linear Algebra and its Applications, vol.484, pp.199-218, 2015.

A. A. Harry-l-trentelman, M. Stoorvogel, and . Hautus, Control theory for linear systems, Communications and Control Engineering Series, p.17, 2002.

L. Úbeda, A combined algorithm for analyzing structural controllability and observability of complex networks, Proceedings of the International Conference on Scientific Computing (CSC), p.57, 2013.

A. Weber, G. Reissig, and F. Svaricek, A linear time algorithm to verify strong structural controllability, IEEE 53rd Annual Conference on, vol.60, p.33, 2014.

S. Weerakkody, X. Liu, and B. Sinopoli, Robust Structural Analysis and Design of Distributed Control Systems to Prevent Zero Dynamics Attacks, 56th IEEE Conference on Decision and Control, p.101, 2017.

J. L. Willems, Structural controllability and observability, In: Systems & control letters, vol.8, p.103, 1986.

M. Sze-zheng-yong, E. Zhu, and . Frazzoli, A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems, Automatica, vol.63, pp.321-329, 2016.

M. Sze-zheng-yong, E. Zhu, and . Frazzoli, Simultaneous input and state estimation with a delay, IEEE 54th Annual Conference on, pp.468-475, 2015.

M. Sze-zheng-yong, E. Zhu, and . Frazzoli, Switching and Data Injection Attacks on Stochastic Cyber-Physical Systems: Modeling, Resilient Estimation and Attack Mitigation, 2017.