In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor-repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast to [8], by introducing slightly stronger definitions of random attractor and repeller, we characterize attractor-repeller pair decompositions and Morse decom...

In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric field theory whose Hamil-tonian, in the deterministic case, coincides with the Lie-derivative of the associated Hamil-tonian flow. The generalized Lyapunov e...

In this paper, global robust stability of stochastic impulsive recurrent neural networks with time-varyingdelays which are represented by the Takagi-Sugeno (T-S) fuzzy models is considered. A novel Linear Matrix Inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy stochastic impulsive recurrent neural...

Abstract. In this paper we study the absolute stability of Lurie control systems with multiple time-delays and nonlinearities, based on the Lyapunov stability theory via the approach of decomposing matrices, by using extended Lyapunov functional, we avoid the use of the stability assumption on the main operator and derive to improve stability criteria, which are strictly less conservative than ...

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of...

In this paper, the stability analysis and control design of Takagi–Sugeno (TS) fuzzy systems subject to uncertain time-delay are addressed. The proposed approach is based on linear matrix inequalities and the Lyapunov–Krasovskii theory, where a new fuzzy weighting-dependent Lyapunov–Krasovskii functional is introduced. By employing the Gu discretization technique and strategies to add slack mat...

This paper provides necessary conditions and sufficient conditions for the (global) Input-to-State Stability property of simple uncertain vehicular-traffic network models under the effect of a PI-regulator. Local stability properties for vehicular-traffic networks under the effect of PI-regulator control are studied as well: the region of attraction of a locally exponentially stable equilibrium...

In this paper, we establish a suucient condition for the stability of a multiclass uid network and queueing network under priority service disciplines. The suucient condition is based on the existence of a linear Lyapunov function, and it is stated in terms of the feasibility of a set of inequalities that are deened by network parameters. In all the networks we have tested, this suucient condit...

This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay s...

We consider the following stochastic bandwidth packing process: the requests for communication bandwidth of different sizes arrive at times t = 0, 1, 2, . . . and are allocated to a communication link using “largest first” rule. Each request takes a unit time to complete. The unallocated requests form queues. Coffman and Stolyar [6] introduced this system and posed the following question: under...