This paper deals with linear time-invariant systems with multiple delays. We present a necessary and sufficient stability condition, expressed in terms of the delay Lyapunov matrix. This result generalizes the well known Lyapunov theorem for delay free linear systems. An illustrative example shows how to apply the presented condition.

This paper presents a Lyapunov-type proof of the Input-toState Stable(ISS) small-gain theorem. The proof given in this paper demonstrates how to construct a Lyapunov function explicitly, which contrasts with existing proofs based on input-output analysis. The Lyapunov functions are constructed by selecting state-dependent scaling functions properly. The construction of Lyapunov functions motiva...

In this paper, the global asymptotic stability of second-order neutral type Cohen-Grossberg neural networks with time-varying delays are investigated. First, by choosing properly variable substitution the system is transformed to first-order differential equation. Second, some sufficient conditions which can ensure the existence and global asymptotic stability of equilibrium point for the syste...

This work provides a generalization of a converse Lyapunov theorem for systems that do not have the regularity property on the invariant sets. As an application , we provide Lyapunov-function like necessary and suucient characterizations for the problem of ISS-disturbance attenuation.

Heart chaotic system and the ability of particle swarm optimization (PSO) method motivated us to benefit the method of chaotic particle swarm optimization (CPSO) to synchronize the heart three-oscillator model. It can be a suitable algorithm for strengthening the controller in presence of unknown parameters. In this paper we apply adaptive control (AC) on heart delay model, also examine the sys...

In this paper, we study the global properties of classic SIS epidemic model with constant recruitment, disease-induced death and standard incidence term. We apply the Poincaré-Bendixson theorem, Dulac’s criterion, and the method of Lyapunov function to establish conditions for global stability. For this system, three Dulac functions and two Lyapunov functions are constructed for the endemic ste...

This paper suggests a new stability analysis theorem dedicated to a class of fuzzy logic control systems. The fuzzy logic control systems consist of nonlinear Single Input-Single Output (SISO) discrete-time processes controlled by Takagi-Sugeno fuzzy logic controllers. The stability analysis is conducted on the basis of Lyapunov’s direct method with quadratic Lyapunov function candidates. The t...

We investigate regularity functions corresponding to a fixed Lyapunov bundle E in the Oseledets multiplicative ergodic theorem for an ergodic flow or diffeomorphism. These functions measure the deviation of the growth in norm of the linearized system from constant exponential growth. In general, Oseledets regularity functions were only known to be Borel measurable. Our main result is that if E ...

in this paper, control of a non-isothermal continuous stirred tank reactor in which two parallel autocatalytic reactions take place has been addressed. the reactor shows chaotic behavior for a certain set of reactor parameters. in order to control the product concentration, an optimal state feedback controller has been designed. since concentrations of reactor species are not measured, an obser...