Related papers: Stability of Fractional Order Switching Systems
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
We study stability issue of reset and impulsive switched systems. We find time constraints (dwell time and flee time) on switching signals which stabilize a given reset switched system. For a given collection of matrices, we find an…
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…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…
This paper addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
In this paper, a fractional derivative with short-term memory properties is defined, which can be viewed as an extension of Caputo fractional derivative. Then, some properties of the short memory fractional derivative are discussed. Also, a…
In this work, we study finite-time stability of switched and hybrid systems in the presence of unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of the system to be finite time stable.…
In this paper, we study the frequency response of uncertain systems using Kharitonov stability theory on first order complex polynomial set. For an interval transfer function, we show that the minimal real part of the frequency response at…
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.
This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…