It is shown that the notion of balancing a state space realization about a stable, isolated equilibrium point can be generalized to systems possessing only a stable invariant regular submanifold of arbitrary dimension, for example, a stable limit cycle.

The sensitivity properties of intermittent control are analysed and the conditions for a limit cycle derived theoretically and verified by simulation. 1 ar X iv :1 70 5. 08 22 8v 1 [ cs .S Y ] 2 2 M ay 2 01 7

Unknown process parameters are identified using limit cycle data of the relay–response curves obtained from single relay feedback test on second order plus dead time (SOPDT) processes. Time domain analytical expressions of these curves are helpful in deriving conditions to estimate process parameters accurately. Identification algorithms are formulated to estimate minimal number of model parame...

We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some re...

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter pro...

The paper analyses the nature of limit cycles induced through the interaction of transformer tap changing and load dynamics. Linearization of a Poincaré map is used to prove local stability. An approximation is introduced which allows the map to be formulated explicitly. An estimate of the region of attraction can then be obtained.

This paper studies the existence of limit cycles in a control system which contains nonlinearities and parametric uncertainties. The existence of limit cycles in a control system with a separable nonlinearity can be predicted using the describing function. In this paper, some of the well-known results developed in the area of parametric robust control are used together with the describing funct...

This paper deals with the stability of an event-based proportional-integral controller. In particular, necessary and sufficient conditions on the controller parameters for the existence of equilibrium points without limit cycles are given for a first-order-plus-dead-time process. Practical issues related to the controller implementation are also addressed. The presented conditions enable a simp...

In this paper, we investigate the number of limit cycles for a class of discontinuous planar differential systems with multiple sectors separated by many rays originating from the origin. In each sector, it is a smooth generalized Liénard polynomial differential system x′ = −y + g1(x) + f1(x)y and y′ = x + g2(x) + f2(x)y, where fi(x) and gi(x) for i = 1, 2 are polynomials of variable x with any...