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Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks, these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
An important design principle for biological oscillators divides the oscillators into two classes: fixed frequency, variable amplitude and fixed amplitude, variable frequency. Because of the interplay of nonlinearity and feedback, both…
We extend the setup in our previous paper to deal with the case in which more than one steady state may exist in feedback configurations. This provides a foundation for the analysis of multi-stability and hysteresis behaviour in high…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…
We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it…
The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low…
The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the…
An integral extension of state-feedback controllers for linear time-varying plants is proposed, which preserves performance of the nominal controller in the unperturbed case. Similar to time-invariant state feedback with integral action,…
Ensuring small-signal stability in power systems with a high share of inverter-based resources (IBRs) is hampered by two factors: (i) device and network parameters are often uncertain or completely unknown, and (ii) brute-force enumeration…
This work provides a design method for achieving a specified level of stability for inverter-based interconnected distributed generation. The stability of parallel connected distributed energy resources determined from a linearized…
In linear systems theory it's a well known fact that a regulator given by the cascade of an oscillatory dynamics, driven by some regulated variables, and of a stabiliser stabilising the cascade of the plant and of the oscillators has the…
This paper is concerned with the problem of robust reliable control for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type. The parameter uncertainties are assumed to be norm-bounded.…
For a general time-varying system, we prove that existence of an "Output Robust Control Lyapunov Function" implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the…
New trajectory-based small-gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous…
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued…
In this paper, we propose a novel dynamic state-feedback controller for polytopic linear parameter-varying (LPV) systems with constant input matrix. The controller employs a projected gradient flow method to continuously improve its control…
Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…