Related papers: Singular Perturbation Theory for a Finite-Dimensio…
The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
This paper presents an anti-windup PI controller, using a saturating integrator, for a single-input single-output stable nonlinear plant, whose steady-state input-output map is increasing. We prove that, under reasonable assumptions, there…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…
A sensitivity conditioning control strategy is analyzed in this paper and it is applied to power electronic converters. The term is used to improve closed loop systems, such as power converters with cascaded inner and outer loop…
Nonlinear systems, such as switching DC-DC boost or buck converters, have rich dynamics. A simple one-dimensional discrete-time model is used to analyze the boost or buck converter in discontinuous conduction mode. Seven different control…
We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this…
This paper studies the emulation-based stabilization of nonlinear networked control systems with two time scales. We address the challenge of using a single communication channel for transmitting both fast and slow variables between the…
This paper presents the analysis and a method to design supplementary damping controllers (SDCs) for synchronous generators considering the effects of saturation limits. Usually such saturations of control signals are imposed in order to…
Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…
We present important use cases and limitations when considering results obtained from Cluster Perturbation Theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of…
Electrical brain stimulation relies on externally applied currents to modulate neural activity, but safety constraints require each stimulation cycle to be charge-balanced, enforcing a zero net injected charge. However, how such…
Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
Self-excited systems arise in numerous applications, such as biochemical systems, fluid-structure interaction, and combustion. This paper analyzes a discrete-time Lur'e system with a piecewise-linear saturation feedback nonlinearity. The…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…
In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions…
We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone…