Uniform Parametric Convergence in the Adaptive Control of Mechanical Systems

Stability analysis of 2D Roesser systems via vector Lyapunov functions

Some sufficient conditions for exponential stability of linear neutral functional differential equations

The general model of distributed parameter switched systems (DPSS) was presented via operator semigroup theory in Hilbert. The problem of output feedback stabilization for DPSS was studied and an exponentially stable observer for any switched law was designed. Meanwhile, a switching strategy and sub-controller, which depend on the observer value, were designed and the sufficient condition of exponential stability of closed-loop DPSS was obtained. When the switching interval time is constrained, the stability analysis for DPSS was also studied via mild solution of an abstract evolution equation and the switching law and sub-controllers were also designed to guarantee that the closed-loop system is exponentially stable.

Maximum Lyapunov exponents and stability criteria of linear systems with variable delay

Exponential stability and periodicity of impulsive cellular neural networks with time delays

In this paper, a general class of nonautonomous Lotka-Volterra dispersal system with discrete and continuous infinite delays is investigated. This class of Lotka-Volterra systems model the diffusion of a single species into n patches by discrete dispersal. By using Schauder's fixed point theorem, we prove the existence of positive periodic solutions of system. The global asymptotical stability of positive periodic solution is discussed and the sufficient conditions for exponential stability are also given. we give an example to illustrate the validity of the results in the end. The conditions we obtained are more general and it can be extended to several special systems.

An energy principle is presented which gives necessary and sufficient conditions for exponential stability for a useful class of continuous linear dissipative systems. The maximal growth rate Ω of an unstable system is shown to be the least upper bound of a certain functional, providing a variational expression for Ω. Applications to the problems of the stability of a stratified viscous incompressible fluid in a gravitational field and the resistive, viscous, incompressible magnetohydrodynamic sheet pinch are discussed.

A graph-theoretic approach to exponential stability of stochastic complex networks with time-varying delays

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

This paper presents a scheduling strategy for a collection of discrete-time networked control systems (NCSs) subjected to communication constraints. Communication constraints under consideration include medium access constraint, network-induced delays and packet-dropouts. A feedback control system with the communication constraints is modelled as a switched delay system which switches on the open-loop and closed-loop models according to whether the feedback control loop gains access to the network or not. Delay-dependent sufficient conditions for exponential stability with L 2 gain performance are developed for the switched system. Based on the stability conditions, sufficient conditions are presented on the existence of scheduling policy that simultaneously stabilizes the collection of NCSs. Simulation on network-based control of unstable batch reactor systems is performed to demonstrated the effectiveness of the proposed scheduling strategy.

Stability and [formula omitted]-gain analysis for switched delay systems: A delay-dependent method

This technical note is concerned with exponential stability analysis of linear time-varying systems represented by the second-order vector differential equations with the singular leading coefficient matrix. Using bounding techniques on the trajectories of the linear time-varying systems, the stability problem of the time-varying systems is transformed to that of the time-invariant systems and a new sufficient condition for exponential stability is derived. The obtained condition can be applied to the nonsingular case and it is proven that the condition for the nonsingular case is superior to a test presented in the recent literature. Analogously, the proposed method is also extended to the stability analysis for a class of linear time-varying systems with delay. By illustrative examples, better results are obtained by the proposed criteria as compared with some results in the literature.

The general model of distributed parameter switched systems (DPSS) was presented by means of operator semigroup theory. On condition that the infinitesimal generator operators of all subsystems satisfy multiplication commutative law, the sufficient conditions of exponential stability and switching laws were obtained for the DPSS consisting of subsystems with the same or various patterns. Meanwhile, the simulation experiment was conducted to test the models and theorem.

The stability analysis and L2‐gain for a class of switched neutral systems with all unstable subsystems are investigated in this paper. By constructing the discretized multiple Lyapunov‐Krasovskii functional and resorting to the time‐driven switching signals, sufficient conditions for exponential stability and weighted L2‐gain are developed for a class of switched neutral systems, where all subsystems are unstable. It should be pointed out that all the Lyapunov‐Krasovskii functional energies are allowed to increase during the running intervals of the active subsystems. Furthermore, all the conditions are formulated in forms of a set of linear matrix inequalities which can be easily solved by using the recently developed interior point method. Finally, two numerical examples are provided to show the effectiveness of the proposed approach.

In this paper, we focus on the exponential stability of stochastic differential equations driven by fractional Brownian motion (fBm) with Hurst parameter $ H\in(1/2, 1) $. Based on the generalized Itô formula and representation of the fBm, some sufficient conditions for exponential stability of a class of SDEs with additive fractional noise are given. Besides, we present a criterion on the exponential stability for the fractional Ornstein-Uhlenbeck process with Markov switching. A numerical example is provided to illustrate our results.