All Outputs (46)

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-

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.

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.

Management of Invasive Insect Species using Optimal Control Theory (2018)
Journal Article
Edholm, C., Tenhumberg, B., Guiver, C., Jin, Y., Townley, S., & Rebarber, R. (2018). Management of Invasive Insect Species using Optimal Control Theory. Ecological Modelling, 381, 36-45. https://doi.org/10.1016/j.ecolmodel.2018.04.011

We discuss the use of optimal control theory to determine the most cost-effective management strategies for insect pests. We use a stage-structured linear population projection model where the modeled control action increases the mortality in one of... Read More about Management of Invasive Insect Species using Optimal Control Theory.

On the strict monotonicity of spectral radii for classes of bounded positive linear operators (2018)
Journal Article
Guiver, C. (2018). On the strict monotonicity of spectral radii for classes of bounded positive linear operators. Positivity, 22, 1173-1190. https://doi.org/10.1007/s11117-018-0566-5

Strict monotonicity of the spectral radii of bounded, positive, ordered linear operators is investigated. It is well-known that under reasonable assumptions, the spectral radii of two ordered positive operators enjoy a non-strict inequality. It is al... Read More about On the strict monotonicity of spectral radii for classes of bounded positive linear operators.

Transfer Functions of Infinite-Dimensional Systems: Positive Realness and Stabilization (2017)
Journal Article
Guiver, C., Logemann, H., & Opmeer, M. R. (2017). Transfer Functions of Infinite-Dimensional Systems: Positive Realness and Stabilization. Mathematics of Control, Signals, and Systems, 29, Article 20 (2017). https://doi.org/10.1007/s00498-017-0203-z

We consider a general class of operator-valued irrational positive-real functions with an emphasis on their frequency-domain properties and the relation with stabilization by output feedback. Such functions arise naturally as the transfer functions o... Read More about Transfer Functions of Infinite-Dimensional Systems: Positive Realness and Stabilization.

Semi-Global Persistence and Stability for a Class of Forced Discrete-Time Population Models (2017)
Journal Article
Franco, D., Guiver, C., Logemann, H., & Perán, J. (2017). Semi-Global Persistence and Stability for a Class of Forced Discrete-Time Population Models. Physica D: Nonlinear Phenomena, 360, 46-61. https://doi.org/10.1016/j.physd.2017.08.001

We consider persistence and stability properties for a class of forced discrete-time difference equations with three defining properties: the solution is constrained to evolve in the non-negative orthant, the forcing acts multiplicatively, and the dy... Read More about Semi-Global Persistence and Stability for a Class of Forced Discrete-Time Population Models.

Low-gain Integral Control for Multi-Input, Multi-Output Linear Systems with Input Nonlinearities (2017)
Journal Article
Guiver, C., Logemann, H., & 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. https://doi.org/10.1109/TAC.2017.2691301

We consider the inclusion of a static anti-windup component in a continuous-time low-gain integral controller in feedback with a multi-input multi-output stable linear system subject to an input nonlinearity (from a class of functions that includes c... Read More about Low-gain Integral Control for Multi-Input, Multi-Output Linear Systems with Input Nonlinearities.

A necessary condition for dispersal driven growth of populations with discrete patch dynamics (2017)
Journal Article
Guiver, C., Packman, D., & Townley, S. (2017). A necessary condition for dispersal driven growth of populations with discrete patch dynamics. Journal of Theoretical Biology, 424, 11-25. https://doi.org/10.1016/j.jtbi.2017.03.030

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populat... Read More about A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

The converging-input converging-state property for Lur’e systems (2017)
Journal Article
Bill, A., Guiver, C., Logemann, H., & Townley, S. (2017). The converging-input converging-state property for Lur’e systems. Mathematics of Control, Signals, and Systems, 29, Article 4 (2017). https://doi.org/10.1007/s00498-016-0184-3

Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur{\textquoteright}e systems, we derive necessary and sufficient conditions for a class of Lur{\textquoteright}e systems to hav... Read More about The converging-input converging-state property for Lur’e systems.

A note on the eigenvectors of perturbed matrices with applications to linear positive systems (2016)
Journal Article
Guiver, C., Hodgson, D., & Townley, S. (2016). A note on the eigenvectors of perturbed matrices with applications to linear positive systems. Linear Algebra and its Applications, 509, 143-167. https://doi.org/10.1016/j.laa.2016.07.010

A result is presented describing the eigenvectors of a perturbed matrix, for a class of structured perturbations. One motivation for doing so is that positive eigenvectors of nonnegative, irreducible matrices are known to induce norms — acting much l... Read More about A note on the eigenvectors of perturbed matrices with applications to linear positive systems.

Stability of Non-Negative Lur'e Systems (2016)
Journal Article
Bill, A., Guiver, C., Logemann, H., & Townley, S. (2016). Stability of Non-Negative Lur'e Systems. SIAM Journal on Control and Optimization, 54(3), 1176-1211. https://doi.org/10.1137/140994599

A stability/instability trichotomy for a class of nonnegative continuous-time Lur'e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute... Read More about Stability of Non-Negative Lur'e Systems.

Simple adaptive control for positive linear systems with applications to pest management (2016)
Journal Article
Guiver, C., Edholm, C., Jin, Y., Mueller, M., Powell, J., Rebarber, R., …Townley, S. (2016). Simple adaptive control for positive linear systems with applications to pest management. SIAM Journal on Applied Mathematics, 76(1), 238-275. https://doi.org/1

Pest management is vitally important for modern arable farming, but models for pest species are often highly uncertain. In the context of pest management, control actions are naturally described by a nonlinear feedback that is generally unknown, whic... Read More about Simple adaptive control for positive linear systems with applications to pest management.

Robust set-point regulation for ecological models with multiple management goals (2015)
Journal Article
Guiver, C., Mueller, M., Hodgson, D., & Townley, S. (2016). Robust set-point regulation for ecological models with multiple management goals. Journal of Mathematical Biology, 72, 1467-1529. https://doi.org/10.1007/s00285-015-0919-7

Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering... Read More about Robust set-point regulation for ecological models with multiple management goals.

The role of population inertia in predicting the outcome of stage-structured biological invasions (2015)
Journal Article
Guiver, C., Dreiwi, H., Filannino, D. M., Hodgson, D., Lloyd, S., & Townley, S. (2015). The role of population inertia in predicting the outcome of stage-structured biological invasions. Mathematical Biosciences, 265, 1-11. https://doi.org/10.1016/j.mbs.2

Deterministic dynamic models for coupled resident and invader populations are considered with the purpose of finding quantities that are effective at predicting when the invasive population will become established asymptotically. A key feature of the... Read More about The role of population inertia in predicting the outcome of stage-structured biological invasions.

Bounds on the dynamics of sink populations with noisy immigration (2014)
Journal Article
Eager, E. A., Guiver, C., Hodgson, D., Rebarber, R., Stott, I., & Townley, S. (2014). Bounds on the dynamics of sink populations with noisy immigration. Theoretical Population Biology, 92, 88-96. https://doi.org/10.1016/j.tpb.2013.12.004

Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics of sink populations are not easily modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined... Read More about Bounds on the dynamics of sink populations with noisy immigration.

Integral control for population management (2014)
Journal Article
Guiver, C., Logemann, H., Rebarber, R., Bill, A., Tenhumberg, B., Hodgson, D., & Townley, S. (2015). Integral control for population management. Journal of Mathematical Biology, 70, 1015-1063. https://doi.org/10.1007/s00285-014-0789-4

We present a novel management methodology for restocking a declining population. The strategy uses integral control, a concept ubiquitous in control theory which has not been applied to population dynamics. Integral control is based on dynamic feedba... Read More about Integral control for population management.