We study the recently introduced notion of output–input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. This paper develops the theory of output–input stability in the multi-input, multi-output setting. We show that output–input stability is a combination of two system properties, one related to detectability and the other to left...

Receding horizon control has recently been used for regulating discrete-time Piecewise Affine (PWA) systems. One of the obstructions for implementation consists in guaranteeing closed-loop stability a priori. This is an issue that has only been addressed marginally in the literature. In this paper we present an extension of the terminal cost method for guaranteeing stability in receding horizon...

The aim of this work is to describe the dynamics a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for local asymptotic stability system’s unique equilibrium. Moreover, we employed Lyapunov functional show that constant equilibrium solution globally asymptotically stable. Furthermore, numerical simulations are shown clarify and exemplif...

asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.from these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. instability condition is obtained and g...

In this paper, a HTLV-I infection model with CTL response is considered. To account for a series of events in infection process, we incorporate a intracellular time delay in the model. We prove that the global dynamics are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 < 1, the infection-free equilibrium...

Ratio-dependent predator—prey models are favored by many animal ecologists recently as more suitable ones for predator—prey interactions where predation involves searching process. However, such models are not well studied in the sense that most results are local stability related. In this paper, we consider the global behaviors of solutions of a ratio-dependent predator—prey systems. Specifica...

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function which is the ratio of two polynomials (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sums of squares certificates and hence such a Lyapunov fun...