Related papers: Controlling Fractional Difference Equations Using …
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the…
Controlling nonlinear systems, especially when data are being used to offset uncertainties in the model, is hard. A natural approach when dealing with the challenges of nonlinear control is to reduce the system to a linear one via change of…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give…
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.
As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that such non-minimum phase zeros cannot be cancelled by unstable…
We investigate a driven, one-dimensional system of colloidal particles in a periodically currogated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory,…
Proportional control can be realized directly through the amplification of analog signals, and it also has the advantage of easy tuning parameters in digital signal control. However, it is difficult for the proportional control to preset…
This paper develops a robust safety-critical control method for nonlinear strictfeedback systems with mismatched disturbances. Using a state transformation and a linear time-varying disturbance observer, the system is converted into a form…
For the fractional order systems \[D^\alpha x(t)=f(x),\quad 0<\alpha\leq 1,\] one can have a critical value of $\alpha$ viz $\alpha_*$ such that the system is stable for $0<\alpha<\alpha_*$ and unstable for $\alpha_*<\alpha\leq 1$. In…