Related papers: Fractional Order Hybrid Systems and Their Stabilit…
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…
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…
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…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
This paper presents some new propositions related to the fractional order $h$-difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order $h$-difference…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
This paper is concerned with the robust design for a class of switching systems from a fractional order control (FOC) perspective. In particular, the tuning of the robust fractional order PI (RFPI) controller is proposed based on phase…
Stability and stabilization analysis of fractional-order linear time-invariant (FO-LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single-order equivalent…
The paper investigates a new hybrid synchronization called modified hybrid synchronization (MHS) via the active control technique. Using the active control technique, stable controllers which enable the realization of the coexistence of…
This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we…
This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals, Lyapunov-based sufficient…
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…
This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…
Hybrid dynamical systems exhibit a diverse array of stability phenomena, each currently addressed by separate Lyapunov-like results. We show that these results are all instances of a single theorem: a Lyapunov function is a morphism from a…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special…
This paper addresses the consensus of a class of uncertain nonlinear fractional-order multi-agent systems (FOMAS). First a fractional non-fragile dynamic output feedback controller is put forward via the output measurements of neighboring…
A novel representation of reset control systems with a zero-crossing resetting law, in the framework of hybrid inclusions, is postulated. The problems of well-posedness and stability of the resulting hybrid dynamical system are…
We generalize notions of passivity and dissipativity to fractional order systems. Similar to integer order systems, we show that the proposed definitions generate analogous stability and compositionality properties for fractional order…