Mathematics

In this paper, global and local uniform asymptotic stability of perturbed dynamical systems is studied by using Lyapunov techniques. The restriction about the perturbed term is that the perturbation is bounded by an integrable function under the assumption that the nominal ...

In this paper we treat the problem of practical feedback stabilization for a class of nonlinear time‐varying systems by means of an observer. A separation principle is given under a restriction about the perturbed term that the perturbation is bounded by an integrable function where the nominal system is supposed to be globally asymptotically stabilizable by a linear feedback. A

In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.

In this paper, we present a practical stability result for perturbed dynamic systems depending on a parameter and we study the practical exponential stability of perturbed triangular systems. These results are applied to show that a separation principle for nonlinear uncertain systems can be achieved and which considers practical global uniform exponential stability.

This work is motivated by problem of practical stability of nonlinear time-varying system˙ () = (, ()) (0) = 0 where ∈ ℝ + , ∈ ℝ and : ℝ + ×ℝ −→ ℝ is continuous in and locally Lipschitz in. We give some sufficient conditions to guarantee practical uniform asymptotic stability in terms of convergence of solutions toward a neighborhood of the origin. An invariance principle is given when the origin is not an equilibrium point. The main result of this paper is illustrated by an example in three dimensional.

In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.

In this paper, we deal with the problem of boundedness of solutions in single-input single-output Lurie system. We prove the boundedness of solutions from the stability of zero dynamics under a restriction on the nonlinearity. The linear block is supposed to be of relative degree one or two, stabilizable by high-gain output feedback and not necessary minimum phase. The nonlinearity is required to have the stiffening property.

We establish some new nonlinear Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of differential equations. Example of applying these inequalities to derive the properties of BVPs is also given.

In this paper we treat the problem of practical feedback stabilization for a class of nonlinear time‐varying systems by means of an observer. A separation principle is given under a restriction about the perturbed term that the perturbation is bounded by an integrable function where the nominal system is supposed to be globally asymptotically stabilizable by a linear feedback. A practical stability approach is obtained. Furthermore, we give an example to show the applicability of our result.

In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.

In this paper we propose sufficient conditions for the robust stability of time-invariant uncertain piecewise-linear systems using homogeneous polynomial Lyapunov functions. The proposed conditions are expressed in terms of linear matrix inequalities, which can be numerically determined. We solve the stabilization of piecewise uncertain linear control systems by using state piecewise-linear feedback. We propose an illustrative example to show the efficiency of the proposed approach.

This paper deals with the problem of the global stabilization for a class of cascade nonlinear control systems. It is well known that, in general, the global asymptotic stability of the cascaded subsystems does not imply the global asymptotic stability of the composite closed-loop system. In this paper, we give additional sufficient conditions for the global stabilization of a cascade nonlinear system. In particular, we consider a class of Takagi-Sugeno (TS) fuzzy cascaded systems. Using the so-called parallel distributed compensation (PDC) controller, we prove that this class of systems can be globally asymptotically stable. An illustrative example is given to show the applicability of the main result.

The goal of this paper is twofold. The first part presents a converse Lyapunov theorem for the notion of uniform practical exponential stability of nonlinear differential equations in presence of small perturbation. This class of nonlinear differential equations can be viewed as parametric differential equations. The second part provides the classical perturbation method of seeking an approximate solution as a finite Taylor expansion of the exact solution. The practical asymptotic validity on the approximate is established on infinite-time interval. Finally, we give a numerical example to prove the validity of our methods.

Olive mill wastewater (OMW) constitutes a major environmental problem for Mediterranean countries, where most of the world olive oil production takes place. The recycling of the OMW and its use as water for irrigation in agriculture, provided that its impact on soil and plant is established, is an attractive possibility for the Mediterranean countries. Investigations were performed on the influence of agronomic application of OMW (amount applied: 30, 60, 100 and 150 m 3 ha À1) in a field of olive trees on trees characters (photosynthesis, root-soluble carbohydrate and root colonisation), soil properties, and soil microbial community structure. Specific attention was paid to arbuscular mycorrhizal (AM) fungi. The soil fatty acid methyl ester (FAME) 16:1o5 was used to quantify biomass of AM fungi and the root FAME 16:1o5 analysis was used as index for the development of colonisation in the olive trees roots. A significant increase in organic C, C/N ratio, extractable phosphorus and exchangeable potassium was found after one year of agronomic application of OMW. The development of saprophytic fungi was significantly higher in the OMW amended soils, whereas the abundance of the soil FAME 16:1o5, root FAME 16:1o5, photosynthetic rates and the amount of the total root-soluble carbohydrate were decreased significantly after agronomic application of OMW. A principal component analysis (PCA) of the trees characteristics profiles showed discrimination between the nonirrigated and the OMW irrigated olive trees. These findings suggest that the altering functioning of arbuscular mycorrhizas should be considered as potential factors mediating olive trees responses to agronomic application of OMW when the OMW dose applied is higher than 30 m 3 ha À1. To our knowledge, this is the first report of alterations in the soil FAME 16:1o5 and root FAME 16:1o5 due to land spreading of OMW.

In this paper, we study the stability problem of nonlinear dynamical control systems. We consider continuous-time dynamical systems whose nominal part is stable and whose perturbed part (uncertainties) is norm-bounded by a positive function. Under some conditions on the perturbation, by using Lyapunov techniques, we show that the system can be uniformly asymptotically stable by a continuous controller.

In this paper we deal with the problem of absolute stabilization for Lur'e systems with time-varying delay in a range. An appropriate Lyapunov-Krasovskii functional is proposed to investigate the delay-range-dependant stabilization problem.The time-varying delay is assumed to belong to an interval and no restriction on its derivative is needed. Some relaxation matrices are introduced, which allow the delay to be a fast time-varying function. Furthermore, a numerical example is given to prove effectiveness of our main result.