Problem Of Practical Stabilization Research Articles

Prescribed-time practical stabilization via majorant systems

This paper provides a design methodology of simple control laws to solve the prescribed-time practical stabilization problem for a class of pseudo-linear systems with a single input, also unstable, subject to perturbations, nonlinear and discontinuous, but bounded. The perturbations on the dynamic matrix, such as a ratio of multi-affine polynomials of nonlinear functions or parameters, are not triangular, and a perturbation on the input of multiplicative type is also considered. The stated methodology is based on the majorant systems approach with optimized quadratic Lyapunov functions. The main advantages of the proposed control laws consist in the simplicity of their design and implementation and the reliable performance. Indeed, these control laws depend on a single design parameter, have constant gains, and guarantee the practical convergence with a prescribed relative error, also after a prescribed time. Some examples, also an engineering one, are provided to validate the obtained theoretical results and show the effectiveness and efficiency of the proposed control laws.

Global practical stabilization of the double integrator system with an imperfect sensor and subject to a bounded disturbance

This paper is concerned with global practical stabilization of the double integrator system with an imperfect sensor and subject to an additive bounded output disturbance. The imperfect sensor nonlinearity possesses the nonlinear characteristics of saturation and dead zone. Because of the presence of output dead zone and the additive disturbance, the states cannot be expected to driven into an arbitrarily small neighborhood of the origin. To solve the global practical stabilization problem, we proposes a low gain-based linear dynamic output feedback law, under which the first state enters and remains in a bounded set whose size is depended on the bound of disturbance and the range of dead zone and the second state enters and remains in a pre-specified arbitrarily small set, both in finite time. Simulation results illustrate the effectiveness of our proposed control method.

Partial stability analysis of linear time-varying perturbed stochastic systems via a refined integral inequality

The Lyapunov approach is one of the most effective and efficient means of studying the partial stability of stochastic systems. A number of authors have analysed the partial practical stability of stochastic differential equations using Lyapunov techniques. Nevertheless, no results are concerned with the partial stability of stochastic systems based on the knowledge of the solution of the system explicitly. This paper has been concerned with the problem of partial practical stability for linear time-varying stochastic perturbed systems. Necessary and sufficient conditions for partial practical uniform exponential stability are given based on generalised Gronwall inequalities, in particular of Gamidov's type. An example is developed to illustrate the obtained results.

Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays

This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria.

Practical exponential stability of hybrid impulsive stochastic functional differential systems with delayed impulses

SummaryThis paper is concerned with the problem of practical exponential stability for hybrid impulsive stochastic functional differential systems with delayed impulses, which comprise three classes of systems: the systems with unstable continuous stochastic dynamics and stable discrete dynamics, the systems with stable continuous stochastic dynamics and unstable discrete dynamics, and the systems where both the continuous stochastic dynamics and the discrete dynamics are stable. By using the Lyapunov‐Razumikhin approach, several new sufficient conditions for the practical exponential stability are established for each class of systems. It shows that the stabilizing and destabilizing delayed impulses that satisfy some conditions on their frequency and amplitude can stabilize the systems with unstable continuous stochastic dynamics in the practical exponential stability sense and ensure the practical exponential stability of the systems with stable continuous stochastic dynamics, respectively. Conversely, if the continuous stochastic dynamics are practically exponentially stable and the delayed impulses are stabilizing, then the systems can be practically exponentially stable regardless of the restrictions on the delayed impulses frequency and amplitude. Finally, two numerical examples are presented to illustrate the efficiency of the results.

Passivating Grain Boundary Defects with Tris(hydroxymethyl)aminomethane to Achieve Efficient and Stable Tin-Based Perovskite Solar Cells

Although tin (Sn)-based perovskite is regarded as a good substitute for a lead-based analogue due to its environmental friendliness and suitable band gap, Sn-based perovskite solar cells (PSCs) still need to overcome practical stability and efficiency problems. Here, a passivation material tris(hydroxymethyl)aminomethane (THAM) with amino and multihydroxyl groups is added into the formamidinium tin iodide (FASnI3) perovskite to reduce the defect state density and unnecessary nonradiative recombination of the film, which eventually not only improves the light absorption ability and film crystallinity but also inhibits the oxidation of Sn2+. Applications of the THAM-doped FASnI3 perovskite films into PSCs acquire a high power conversion efficiency of 9.18%. Moreover, the storage stabilities of PSCs are obviously prolonged because of the improved Sn-based perovskite film quality, showing excellent stability of 550 h to keep 85% of its initial efficiency (in an N2 environment).

Practical Stability for Conformable Time-Delay Systems

This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm the practical exponential stability and design of the proposed class of systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These conditions are expressed in the form of linear matrix inequalities (LMI) which could be solved by using solvers in LMI Toolbox of MATLAB. Two numerical examples are given to illustrate the applicability of the proposed results.

Global Practical Stabilization of the Double Integrator System In the Presence of Output Saturation and a Bounded Disturbance

In this paper we consider the problem of global practical stabilization of the double integrator system in the presence of output saturation and a bounded disturbance additive to the output. Because of the disturbance in the output, not all system states can be driven into an arbitrarily small set, as in the usual practical stabilization problem, the output can only be driven into a bounded set whose size is dependent on the bound of the disturbance. It is shown that there exist linear feedback laws that globally practically stabilize the double integrator system in the presence of output saturation and the bounded output disturbance, and we propose linear low gain based dynamic output feedback laws to solve the global practical stabilization problem. Simulation results illustrate the effectiveness of the proposed control design.

Generalized integral inequality and application on partial stability analysis

The method of Lyapunov is one of the most effective methods for the analysis of the partial stability of dynamical systems. Different authors develop the problem of partial practical stability based on Lyapunov techniques. In this paper, we investigate the partial practical stability of linear time-invariant perturbed systems based on the integral inequalities of the Gronwall type, in particular of Gamidov?s type. We derive some sufficient conditions that guarantee global practical uniform exponential stability with respect to a part of the variables of linear time-invariant perturbed systems. Also, we have developed the local partial practical stability of nonlinear systems. Further, we provide two examples to support our findings.

Dynamic event-triggered practical stabilization of random suspension system based on immersion and invariance

This article investigates the practical stabilization problem of random quarter-car active suspension systems. An adaptive dynamic event-trigger strategy is proposed to stabilize the states of vehicle suspension in response to system uncertainty and controller area network resource constraints. Moreover, the model of random active suspension systems is extended to the general random robot systems; the controller is developed with the aid of a double dynamic surface filter, immersion and invariance (I&I) techniques, and event-triggered mechanisms. The results show that the semi-global stability of error systems is achieved, and there are some improvements in triggering times and adaptive estimation performance under the control framework. Finally, simulation comparison results are provided to prove the advantages of the proposed scheme.

Lyapunov matrix‐based method to global robust practical exponential r‐stability for a class of delayed continuous‐time nonlinear systems: Theory and applications

AbstractThis article involves the problem of global robust practical exponential ‐stability for a class of delayed continuous‐time nonlinear systems. By proposing a method based on Lyapunov matrix, a global robust practical exponential ‐stability criterion of the considered systems is established. The criteria are expressed as uncomplicated linear matrix inequalities. Therefore, standard calculation software can be used for verification. In addition, the proposed method is applied to the practical stabilization problem of three‐state turbocharged diesel engine model, and a good control effect is obtained.

Practical Stability and Event-Triggered Load Frequency Control of Networked Power Systems

Practical stability analysis for delayed systems is discussed. Weak practical stability conditions are derived by using Halanay’s inequality and the Lyapunov method. The results are applied to address the problem of practical stability of a power system over a delay-induced communication network. An event-detection-based control scheme is proposed to reduce the communication burdens. Based on the obtained practical stability conditions and the proposed event-detection scheme, sufficient practical stability conditions for load frequency control of a networked power system are given. Furthermore, a new design approach to the event-detection-based controller is presented. Finally, a numerical simulation is given to show the effectiveness and advantage of the obtained results.

Practical adaptive finite-time stabilization for a class of second-order systems

This paper considers the practical adaptive finite-time stabilization problem for a class of second-order systems. Based on the adding a power integrator technique and the adaptive method, a novel adaptive control strategy is presented to assure the trajectories of the closed-loop systems converge to a small neighborhood of the origin in a finite time. Under the adaptive control strategy, the dynamical change of control gain is dependent on the cases whether the state trajectories enter or leave a pre-designed domain or not. In addition, the practical finite-time stability (PFTS) of systems is testified via utilizing the Lyapunov method and adaptive mechanism. Last of all, the validity of the obtained practical adaptive finite-time algorithm is verified via simulation results.

Practical stability of switched homogeneous positive nonlinear systems: Max-separable Lyapunov function method

The practical stability problem of switched homogeneous positive nonlinear systems (SHPNS) is addressed in this study, which includes two instances in terms of continuous-time and discrete-time. Sufficient conditions are presented by using the max-separable Lyapunov function (MSLF) approach, such that each solution of SHPNS is practically stable. The distinction between the existing results and the obtained results is that ours are not only relatively concise but also easily verifiable, and the theoretical results are also extended to a more general case without restricting the systems to be positive. Eventually, a pair of examples are proposed to explain the approach’s validity.

Practical exponential stability of stochastic delayed systems with G-Brownian motion via vector G-Lyapunov function

This paper deals with practical stability problem for nonlinear stochastic delayed systems with G-Brownian motion (GSDSs). Practical stability can describe qualitative behavior and quantitative properties of systems in comparison with traditional Lyapunov stability theory. By employing stochastic analysis technique, Razumikhin-type theorem and vector G-Lyapunov function, new sufficient conditions for pth moment practical exponential stability of GSDSs are proposed. Finally, two examples are presented to verify the feasibility of theoretical results.

On the Practical Compensator Design of Time-Varying Perturbed Systems in Hilbert Spaces

In this paper, we treat the problem of practical feedback stabilization for a class of nonlinear infinite-dimensional control systems by means of an observer. A compensator design is given under a restriction of the perturbed term that the perturbations is bounded by the sum of a Holder continuous function and a Lipschitz function where the nominal system is supposed to be exponentially stabilizable by a linear feedback. The results are illustrated with an example.

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

This paper considers the practical asymptotic stabilization of adesired equilibrium point in discrete-time switched affine systems.The main purpose is to design a state feedback switching rule forthe discrete-time switched affine systems whose parameters can beextracted with less computational complexities. In this regard,using switched Lyapunov functions, a new set of sufficientconditions based on matrix inequalities are developed to solve thepractical stabilization problem. For any size of the switched affinesystem, the derived matrix inequalities contain only one bilinearterm as a multiplication of a positive scalar and a positivedefinite matrix. It is shown that the practical stabilizationproblem can be solved via a few convex optimization problems,including Linear Matrix Inequalities (LMIs) through gridding of ascalar variable interval between zero and one. The numericalexperiments on an academic example and a DC-DC buck-boost converter,as well as comparative studies with the existing works, prove thesatisfactory operation of the proposed method in achieving betterperformances and more tractable numerical solutions.

Local practical stabilization for a class of discrete-time switched affine systems

This paper deals with the study of discrete-time switched affine systems. While generally the literature is focused on the global (practical) stabilization problem, there are classes of switched affine systems that can be stabilized only locally. In this paper we deal with such a class of switched affine systems. More precisely, we consider switched affine systems with decoupled switching in the state matrix and the affine input term. For this particular class of systems, a switching control law is designed and conditions ensuring the system local practical stability are provided. A qualitative approach is given based on the existence of a stabilizing linear state feedback. These results are illustrated using a numerical example.

Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via state-dependent switching rules. Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid. These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type. In some cases, the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function. In this paper, we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently. The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size. Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size, i.e., a purely numerical method and a numerical-analytical one. In the former, both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities. The latter is established on a principle that the attractiveness of a set implies its invariance. Thus, the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension. Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

Розрахунок оптимальних параметрів коректувальних елементів в індукційних системах прискорення

The formulations of a number of optimization problems for a linear induction acceleration system with respect to the adjustment parameters are considered. The dynamics of the transverse motion of electrons in the horizontal plane is investigated in the presence of given energy values for each resonator period: the particles at the initial moment of time are somewhat displaced relative to the accelerator axis (we neglect the displacements of the ends of the solenoids and the centers of the accelerating gaps relative to the accelerator axis). A connection is established between the initial and final coordinates and the components of the momentum. The presence of parasitic electric and magnetic fields arising as a result of the displacement of particles relative to the axis of the accelerator, which change the transverse components of the pulses, is taken into account. For the mathematical formulation of problems, in order to apply algorithms of practical stability, the original difference model of the induction system was converted to a linear form. By introducing into consideration the vector of parameters, the scatter of phase coordinates, and tolerances on the parameters, the problem of calculating the tolerances for given linear constraints on the scatter of phase coordinates for the corresponding inhomogeneous system is formulated. For the case of nonlinear dynamic constraints on the spread of the vector of phase coordinates, it is proposed to approximate a convex closed set by tangent hyperplanes. Numerical estimation of the range of tolerances for the parameters of correcting elements is reduced to the problems of practical stability of discrete parametric systems. In this case, the region of the initial conditions on the state vector, the tolerances on the parameters, are given structurally in the form of an ellipsoid, which makes it possible to numerically solve the original problem as an extremal one. From the standpoint of practical stability in the corresponding space of functions, the problem of assessing the range of tolerances for the parameters of correcting elements in the presence of specified restrictions on the spread of the quality criterion is considered. Attention is focused on an important class of problems of numerical modelling of a linear induction acceleration system − problems of practical stability. Numerical estimation of the region of initial displacements of the transverse coordinates of the linear induction acceleration system in the given structures in the presence of linear constraints on the vector of phase coordinates in dynamics is carried out. Key words: modeling, induction system of acceleration, solenoid, parameters, elements of correction, optimization, stability