# Dr Chris Guiver

## Profile

I am an applied mathematician with research interests in mathematical control theory and its applications to biology and ecology. Roughly, these interests lie in what is termed applied dynamical systems, and draws upon real, complex and applied functional analysis as well as dynamical systems theory. Many examples of biological systems are so-called positive systems, meaning that their dynamics evolve in positive cones (representing necessarily nonnegative quantities, such as abundance), not linear spaces. There is much beautiful and useful mathematics associated with positive systems, I believe, and owing to potential applications I am interested in control theory within this framework.

I started as a lecturer in Bath in January 2016, before which I was a research post-doc at the University of Exeter. I obtained my PhD, also from Bath, in 2012.

### Publications

Guiver, C., Logemann, H. and Opmeer, M., 2017. Forthcoming. Transfer Functions of Infinite-Dimensional Systems: Positive Realness and Stabilization. *Mathematics of Control Signals and Systems*

Guiver, C., Logemann, H. and Townley, S., 2017. Low-gain Integral Control for Multi-Input, Multi-Output Linear Systems with Input Nonlinearities. *IEEE Transactions on Automatic Control*, 62 (9), 4776 - 4783.

Franco, D., Guiver, C., Logemann, H. and Peran, J., 2017. Semi-Global Persistence and Stability for a Class of Forced Discrete-Time Population Models. *Physica D: Nonlinear Phenomena*

Guiver, C., Packman, D. and Townley, S., 2017. A necessary condition for dispersal driven growth of populations with discrete patch dynamics. *Journal of Theoretical Biology*, 424, pp. 11-25.

Bill, A., Guiver, C., Logemann, H. and Townley, S., 2017. The converging-input converging-state property for Lur'e systems. *Mathematics of Control Signals and Systems*, 29 (1), 4.

Guiver, C., Hodgson, D. and Townley, S., 2016. A note on the eigenvectors of perturbed matrices with applications to linear positive systems. *Linear Algebra and its Applications*, 509, pp. 143-167.

Bill, A., Guiver, C., Logemann, H. and Townley, S., 2016. Stability of Non-Negative Lur'e Systems. *SIAM Journal on Control and Optimization*, 54 (3), pp. 1176-1211.

Guiver, C., Mueller, M., Hodgson, D. and Townley, S., 2016. Robust set-point regulation for ecological models with multiple management goals. *Journal of Mathematical Biology*, 72 (6), pp. 1467-1529.

Guiver, C., Edholm, C., Jin, Y., Mueller, M., Powell, J., Rebarber, R., Tenhumberg, B. and Townley, S., 2016. Simple adaptive control for positive linear systems with applications to pest management. *SIAM Journal on Applied Mathematics*, 76 (1), pp. 238-275.

Guiver, C., Logemann, H. and Townley, S., 2016. Simple adaptive feedback control for positive state control systems. *In*: *The 5th International Symposium on Positive Systems*, 2016-09-14 - 2016-09-16, Universita Campus Bio-Medico di Roma.

Guiver, C., Dreiwi, H., Filannino, D. M., Hodgson, D., Lloyd, S. and Townley, S., 2015. The role of population inertia in predicting the outcome of stage-structured biological invasions. *Mathematical Biosciences*, 265, pp. 1-11.

Guiver, C., Logemann, H., Rebarber, R., Bill, A., Tenhumberg, B., Hodgson, D. and Townley, S., 2015. Integral control for population management. *Journal of Mathematical Biology*, 70 (5), pp. 1015-1063.

Guiver, C., Mueller, M., Lloyd, S. and Townley, S., 2015. *The Tour de Maths Reaches Out in Cornwall.* [Non-academic press]

Guiver, C. and Opmeer, M.R., 2014. Model reduction by balanced truncation for systems with nuclear Hankel operators. *SIAM Journal on Control and Optimization (SICON)*, 52 (2), pp. 1366-1401.

Eager, E. A., Guiver, C., Hodgson, D., Rebarber, R., Stott, I. and Townley, S., 2014. Bounds on the dynamics of sink populations with noisy immigration. *Theoretical Population Biology*, 92, pp. 88-96.

Guiver, C., Hodgson, D. and Townley, S., 2014. Positive state controllability of positive linear systems. *Systems & Control Letters*, 65 (1), pp. 23-29.

Bill, A., Guiver, C., Logemann, H. and Townley, S., 2014. A stability/instability trichotomy for non-negative Lur’e systems.

Guiver, C. and Townley, S., 2014. Controllability for positive discrete–time linear systems with p ositive state.

Guiver, C. and Opmeer, M. R., 2013. Error bounds in the gap metric for dissipative balanced approximations. *Linear Algebra and its Applications*, 439 (12), 3659–3698.

Guiver, C. and Opmeer, M. R., 2013. Bounded real and positive real balanced truncation for infinite-dimensional systems. *Mathematical Control and Related Fields*, 3 (1), pp. 83-119.

Guiver, C., 2012. *Model Reduction by Balanced Truncation.* Thesis (Doctor of Philosophy (PhD)). University of Bath.

Guiver, C. and Opmeer, M. R., 2011. A counterexample to "positive realness preserving model reduction with H-infinity norm error bounds". *IEEE Transactions on Circuits and Systems. Part I: Regular Papers*, 58 (6), pp. 1410-1411.

Guiver, C. and Opmeer, M. R., 2010. Non-dissipative boundary feedback for Rayleigh and Timoshenko beams. *Systems & Control Letters*, 59 (9), pp. 578-586.