Related papers: Basic Properties and Stability of Fractional-Order…
The paper deals with the stability analysis of time-delay reset control systems, for which the resetting law is assumed to satisfy a time-dependent condition. A stability analysis of the closed-loop system is performed based on an…
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…
The discrete-time robust repetitive control (RC, or repetitive controller, also designated RC) problem for nonlinear systems is both challenging and practical. This paper proposes a discrete-time output-feedback RC design for a class of…
This paper deals with feedback control of fractional-order Chua's system. The fractional-order Chua's system with total order less than three which exhibit chaos as well as other nonlinear behavior and theory for control of chaotic systems…
Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was…
Sufficient condition for the stability of a fractional order semi-linear system with multi-time delay is proposed.
A general controller scheme for stabilizing a non-linear system, which has its origin from the linear system theory, is proposed in this paper. The proposed controller can stabilize the non-linear system subjected to initial conditions. An…
In this letter, we prove that under mild conditions, the scaled graph of a reset control system is bounded by the scaled graph of its underlying base linear system, i.e., the system without resets. Building on this new insight, we establish…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
In this paper, we study a class of multi-order fractional nonlinear delay systems. Our main contribution is to show the (local or global) Mittag-Leffler stability of systems when some structural assumptions are imposed on the "vector…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
In this paper, we address the problem of stability and frequency regulation of a recently proposed inverter. In this type of inverter, the DC-side capacitor emulates the inertia of a synchronous generator. First, we remodel the dynamics…
Integer-order calculus often falls short in capturing the long-range dependencies and memory effects found in many real-world processes. Fractional calculus addresses these gaps via fractional-order integrals and derivatives, but…
Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results…
Impulsive dynamical systems is a well-established area of dynamical systems theory, and it is used in this work to analyze several basic properties of reset control systems: existence and uniqueness of solutions, and continuous dependence…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
In this paper, a linearized asymptotic stability result for a Caputo-Katugampola fractional-order systems is described. An application is given to demonstrate the validity of the proposed results.
In this paper, synchronization of fractional order Coullet system with precise and also unknown parameters are studied. The proposed method which is based on the adaptive backstepping, has been developed to synchronize two chaotic systems…
When the order of an integrator is a complex number, the integrator is called a complex fractional order integrator (CFOI). The impulse response invariant discretization (IRID) method is proposed to approximately discretize the CFOI. The…
This paper addresses a phenomenon caused by resetting only one of the two states of a so-called second order "Constant in gain Lead in phase" (CgLp) element. CgLp is a recently introduced reset-based nonlinear element, bound to circumvent…