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Stabilisation by adaptive feedback control for positive difference equations with applications in pest management (2022)
Journal Article
Edholm, C., Guiver, C., Rebarber, R., Tenhumberg, B., & Townley, S. (2022). Stabilisation by adaptive feedback control for positive difference equations with applications in pest management. SIAM Journal on Control and Optimization, 60(4), 2214-2245. https://doi.org/10.1137/21m1398240

An adaptive feedback control scheme is proposed for stabilising a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers, and contains substantial robustness with respect... Read More about Stabilisation by adaptive feedback control for positive difference equations with applications in pest management.

Quantifying the per-capita contribution of all components of a migratory cycle: a modelling framework (2022)
Journal Article
Smith, P., Guiver, C., & Adams, B. (2022). Quantifying the per-capita contribution of all components of a migratory cycle: a modelling framework. Ecological Modelling, 471, Article 110056. https://doi.org/10.1016/j.ecolmodel.2022.110056

Migratory species make use of different habitats and pathways at different life stages, and in different seasons. Ecological management strategies proposed for migratory species should acknowledge the importance of each component of the migratory cyc... Read More about Quantifying the per-capita contribution of all components of a migratory cycle: a modelling framework.

An equivalence framework for an age-structured multi-stage representation of the cell cycle (2022)
Journal Article
Kynaston, J. C., Guiver, C., & Yates, C. A. (2022). An equivalence framework for an age-structured multi-stage representation of the cell cycle. Physical Review E, 105(6), https://doi.org/10.1103/PhysRevE.105.064411

We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multi... Read More about An equivalence framework for an age-structured multi-stage representation of the cell cycle.

The circle criterion for a class of sector-bounded dynamic nonlinearities (2022)
Journal Article
Guiver, C., & Logemann, H. (2022). The circle criterion for a class of sector-bounded dynamic nonlinearities. Mathematics of Control, Signals, and Systems, 34, 461-492. https://doi.org/10.1007/s00498-022-00324-3

We present a circle criterion which is necessary and sufficient for absolute stability with respect to a natural class of sector-bounded nonlinear causal operators. This generalized circle criterion contains the classical result as a special case. F... Read More about The circle criterion for a class of sector-bounded dynamic nonlinearities.

Incremental input-to-state stability for Lur’e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing (2021)
Journal Article
Gilmore, M., Guiver, C., & Logemann, H. (2021). Incremental input-to-state stability for Lur’e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing. Journal of Differential Equations, 300, 692-733. https://doi.org/10.1016/j.jde.2021.08.009

We prove (integral) input-to-state stability results for a class of forced Lur’e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur’e differential equations. The latter provide a basi... Read More about Incremental input-to-state stability for Lur’e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing.

Persistence and stability for a class of forced positive nonlinear delay-differential systems (2021)
Journal Article
Franco, D., Guiver, C., & Logemann, H. (2021). Persistence and stability for a class of forced positive nonlinear delay-differential systems. Acta applicandae mathematicae, 174(1), Article 1 (2021). https://doi.org/10.1007/s10440-021-00414-5

Persistence and stability properties are considered for a class of forced positive non-linear delay-differential systems which arise in mathematical ecology and other applied contexts.The inclusion of forcing incorporates the effects of control actio... Read More about Persistence and stability for a class of forced positive nonlinear delay-differential systems.

A switching feedback control approach for persistence of managed resources (2021)
Journal Article
Franco, D., Guiver, C., Smith, P., & Townley, S. (2022). A switching feedback control approach for persistence of managed resources. Discrete and Continuous Dynamical Systems - Series B, 27(3), 1765-1787. https://doi.org/10.3934/dcdsb.2021109

An adaptive switching feedback control scheme is proposed for classes of discrete-time, positive difference equations, or systems of equations. In overview, the objective is to choose a control strategy which ensures persistence of the state, consequ... Read More about A switching feedback control approach for persistence of managed resources.

Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities (2021)
Journal Article
Gilmore, M. E., Guiver, C., & Logemann, H. (2022). Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities. Mathematical Control and Related Fields, 12(1), 17-47. https://doi.org/10.3934/mcrf.2021001

A low-gain integral controller with anti-windup component is presented for exponentially stable, linear, discrete-time, infinite-dimensional control systems subject to input nonlinearities and external disturbances. We derive a disturbance-to-state... Read More about Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities.

Dynamic observers for unknown populations (2020)
Journal Article
Guiver, C., Poppelreiter, N., Rebarber, R., Tenhumberg, B., & Townley, S. (2021). Dynamic observers for unknown populations. Discrete and Continuous Dynamical Systems - Series B, 26(6), 3279-3302. https://doi.org/10.3934/dcdsb.2020232

Dynamic observers are considered in the context of structured population modeling and management. Roughly, observers combine a known measured variable of some process with a model of that process to asymptotically reconstruct the unknown state variab... Read More about Dynamic observers for unknown populations.

On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition (2020)
Journal Article
Franco, D., Guiver, C., Logemann, H., & Perán, J. (2020). On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition. Electronic Journal of Qualitative Theory of Differential Equations, 1-15. https://doi.org/10.14232/ejqtde.2020.1.76

We study the size of the global attractor for a delay differential equation with unimodal feedback. We are interested in extending and complementing a dichotomy result by Liz and Röst, which assumed that the Schwarzian derivative of the nonlinear fee... Read More about On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition.

Infinite-dimensional Lur'e systems with almost periodic forcing (2020)
Journal Article
Gilmore, M. E., Guiver, C., & Logemann, H. (2020). Infinite-dimensional Lur'e systems with almost periodic forcing. Mathematics of Control, Signals, and Systems, 32, 327-360. https://doi.org/10.1007/s00498-020-00262-y

We consider forced Lur’e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial-differential equa-tions are known to belong to this class of infinite-dime... Read More about Infinite-dimensional Lur'e systems with almost periodic forcing.

Semi-global incremental input-to-state stability of discrete-time Lur'e systems (2020)
Journal Article
Gilmore, M., Guiver, C., & Logemann, H. (2020). Semi-global incremental input-to-state stability of discrete-time Lur'e systems. Systems and Control Letters, 136, Article 104593. https://doi.org/10.1016/j.sysconle.2019.104593

We present sufficient conditions for semi-global incremental input-to-state stability of a class of forced discrete-time Lur'e systems. The results derived are reminiscent of well-known absolute stability criteria such as the small gain theorem and t... Read More about Semi-global incremental input-to-state stability of discrete-time Lur'e systems.

A circle criterion for strong integral input-to-state stability (2019)
Journal Article
Guiver, C., & Logemann, H. (2020). A circle criterion for strong integral input-to-state stability. Automatica, 111, Article 108641. https://doi.org/10.1016/j.automatica.2019.108641

We present sufficient conditions for integral input-to-state stability (iISS) and strong iISS of the zero equilibrium pair of continuous-time forced Lur'e systems, where by strong iISS we mean the conjunction of iISS and small-signal ISS. Our main re... Read More about A circle criterion for strong integral input-to-state stability.

Boundedness, persistence and stability for classes of forced difference equations arising in population ecology (2019)
Journal Article
Franco, D., Guiver, C., Logemann, H., & Perán, J. (2019). Boundedness, persistence and stability for classes of forced difference equations arising in population ecology. Journal of Mathematical Biology, 79, 1029-1076. https://doi.org/10.1007/s00285-019-01388-7

Boundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise in a number of ecological and biological contexts. The inclusion of forcing incorporates... Read More about Boundedness, persistence and stability for classes of forced difference equations arising in population ecology.

Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems (2019)
Journal Article
Gilmore, M. E., Guiver, C., & Logemann, H. (2020). Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems. International Journal of Control, 93(12), 3026-3049. https://doi.org/10.1080/00207179.2019.1575528

Incremental stability and convergence properties for forced, infinite-dimensional, discrete-time Lur'e systems are addressed. Lur'e systems have a linear and nonlinear component and arise as the feedback interconnection of a linear control system and... Read More about Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems.

Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties (2019)
Journal Article
Guiver, C., Logemann, H., & Opmeer, M. R. (2019). Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties. SIAM Journal on Control and Optimization, 57(1), 334-365. https://doi.org/10.1137/17M1150426

We consider forced Lur'e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial differential equations are known to belong to this class of infinite-dimensional sys... Read More about Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties.

The generalised singular perturbation approximation for bounded real and positive real control systems (2018)
Journal Article
Guiver, C. (2019). The generalised singular perturbation approximation for bounded real and positive real control systems. Mathematical Control and Related Fields, 9(2), 313-350. https://doi.org/10.3934/mcrf.2019016

The generalised singular perturbation approximation (GSPA) is considered as a model reduction scheme for bounded real and positive real linear control systems. The GSPA is a state-space approach to truncation with the defining property that the trans... Read More about The generalised singular perturbation approximation for bounded real and positive real control systems.

Recent Findings on Strong Integral Input-To-State Stability for Forced Lur'e Systems (2018)
Presentation / Conference Contribution
Guiver, C., & Logemann, H. (2018, September). Recent Findings on Strong Integral Input-To-State Stability for Forced Lur'e Systems. Paper presented at UKACC 12th International Conference on Control (CONTROL), Sheffield, UK

We would like to present recent theoretical results on the strong integral Input-to-State Stability (strong iISS) for the following class of finite-dimensional, continuous-time forced Lur'e systems.

Small-gain stability theorems for positive Lur'e inclusions (2018)
Journal Article
Guiver, C., Logemann, H., & Rüffer, B. (2019). Small-gain stability theorems for positive Lur'e inclusions. Positivity, 23, 249-289. https://doi.org/10.1007/s11117-018-0605-2

Stability results are presented for a class of differential and difference inclusions, so-called positive Lur{\textquoteright}e inclusions which arise, for example, as the feedback interconnection of a linear positive system with a positive set-valued... Read More about Small-gain stability theorems for positive Lur'e inclusions.