Related papers: Basic Properties and Stability of Fractional-Order…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
PI controllers are the most widespread type of controllers and there is an intuitive understanding that if their gains are sufficiently small and of the correct sign, then they always work. In this paper we try to give some rigorous backing…
In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…
The celebrated GKYP is widely used in integer-order control system. However, when it comes to the fractional order system, there exists no such tool to solve problems. This paper prove the FGKYP which can be used in the analysis of problems…
A Fluctuation Theorem (FT), both Classical and Quantum, describes the large-deviations in the approach to equilibrium of an isolated quasi-integrable system. Two characteristics make it unusual: (i) it concerns the internal dynamics of an…
With the increasing penetration of Inverter-Based Resources (IBRs), power system stability constraints must be incorporated into the operational framework, transforming it into stability-constrained optimization. Currently, there exist…
In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller…
Inverter-based microgrids are an important technology for sustainable electrical power systems and typically use droop-controlled grid-forming inverters to interface distributed energy resources to the network and control the voltage and…
In this paper, we present a scheme for uncovering hidden chaotic attrac- tors in nonlinear autonomous systems of fractional order. The stability of equilibria of fractional-order systems is analyzed. The underlying initial value problem is…
This study presents the framework to perform a stability analysis of nonlocal solids whose response is formulated according to the fractional-order continuum theory. In this formulation, space fractional-order operators are used to capture…
This paper presents a complex order filter developed and subsequently integrated into a PID-based controller design. The nonlinear filter is designed with reset elements to have describing function based frequency response similar to that…
This paper addresses nonlinearity in reset elements and their effects. Reset elements are known for having less phase lag compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This…
This study proposes a simple controller design approach to achieve a class of robustness, the so-called iso-damping property. The proposed approach can be executed using only one-shot input/output data. An accurate mathematical model of a…
The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to single Stokes pulse. The dynamic behavior for this fractional model (called the fractional Stokes system) is investigated,…
When electric vehicles (EVs) are integrated into standalone DC microgrids (DCMGs), stability issues arise due to their constant power load (CPL) behavior, which provides negative incremental impedance (NII). In addition, the microgrids…
The frequency response analysis describes the steady-state responses of a system to sinusoidal inputs at different frequencies, providing control engineers with an effective tool for designing control systems in the frequency domain.…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
The existence of a Control Barrier Function (CBF) for a control-affine system provides a powerful design tool to ensure safety. Any controller that satisfies the CBF condition and ensures that the trajectories of the closed-loop system are…
We study the control of networked systems with the goal of optimizing both transient and steady-state performances while providing stability guarantees. Linear proportional-integral (PI) controllers are almost always used in practice, but…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…