Partial stabilisation of non-homogeneous bilinear systems

In this work, we study in a Hilbert state space, the partial stabilisation of non-homogeneous bilinear systems using a bounded control. Necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions. Applications to parabolic and hyperbolic equations are presented.     

Finite-time boundedness and stabilisation of networked control systems with bounded packet dropout

In this paper, the finite-time boundedness and stabilisation problems of a class of networked control systems (NCSs) with bounded packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time boundedness and stability via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump linear systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time boundedness and stabilisation of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Moreover, both sensor-to-controller and controller-to-actuator packet dropouts are considered simultaneously. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.     

Stabilisation and polynomial decay estimate for distributed semilinear systems

In this article, we propose a family of feedback controls that guarantee weak and strong stabilisability for distributed semilinear systems. In the case of strong stabilisation, an optimal decay of the state is estimated. Applications to wave equations are provided.     

Global stabilisation for a class of switched high-order stochastic nonlinear systems

This paper is devoted to the problem of global stabili sation for a class of switched high-order stochastic nonlinear systems under arbitrary switchings. By extending the adding -a -power -integrator technique and choosing an appropriate common Lyapunov function, a common state-feedback controller is explicitly constructed to render the closed-loop system globally asymptotically stable in probability. The effectiveness of the proposed approach is demonstrated by a simulation example.     

Partial stability and stabilisation of Boolean networks

In this paper, we investigate the stability of Boolean networks and the stabilisation of Boolean control networks with respect to part of the system's states. First, an algebraic expression of the Boolean (control) network is derived by the semi-tensor product of matrices. Then, some necessary and sufficient conditions for partial stability of Boolean networks are given. Finally, the stabilisation of Boolean control networks by a free control sequence and a state-feedback control is investigated and the respective necessary and sufficient conditions are obtained. Examples are provided to illustrate the efficiency of the obtained results.     

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.     

Globally uniformly asymptotical stabilisation of time-delay nonlinear systems

Globally uniformly asymptotical stabilisation of nonlinear systems in feedback form with a delay arbitrarily large in the input is dealt with based on the backstepping approach in this article. The design strategy depends on the construction of a Lyapunov–Krasovskii functional. A continuously differentiable control law is obtained to globally uniformly asymptotically stabilise the closed-loop system. The simulation shows the effectiveness of the method.     

Finite-time stabilisation for high-order nonlinear systems with low-order and high-order nonlinearities

This paper considers the finite-time stabilisation for a class of high-order nonlinear systems with both low-order and high-order nonlinearities. Based on the finite-time Lyapunov stability theorem together with the methods of dynamic gain control and adding one power integrator, a state feedback controller with gains being tuned online by two dynamic equations is proposed to guarantee the global finite-time stabilisation of the closed-loop system.     

Asymptotic stabilisation for a class of feedforward input-delay systems with ratios of odd integers

This article addresses the stabilisation problem by state-feedback for a class of feedforward input-delay nonlinear systems with ratios of odd integer powers. The designed controller achieves the global asymptotic stability. Based on the appropriate state transformation of time-delay systems and the Lyapunov method, the problem of controller design can be converted into the problem of finding a parameter which can be obtained by appraising the nonlinear terms of the systems. Finally, three simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this article.     

Output feedback stabilisation for uncertain nonlinear time-delay systems subject to input constraints

Robust stabilisation of a class of imperfectly known systems with time-varying time-delays via output feedback is investigated. The systems addressed are composed of a nonlinear nominal system influenced by nonlinear perturbations which may be time-, state-, delayed state- and/or input-dependent. The output of the system is modelled by a nonlinear function, which may depend on the delayed states, and inputs, together with a feed-through term. Using bounding information on the perturbations, in terms of specified growth conditions, classes of unconstrained and constrained output feedback controllers are designed in order to guarantee a prescribed stability property for the closed-loop systems, provided appropriate stability criteria hold. Two stability criteria are given: one in terms of a linear matrix inequality (LMI) and the other is algebraic in nature, obtained using a Ger?gorin Theorem.     

Finite-time stabilisation for a class of output-constrained nonholonomic systems with its application

This paper studies the problem of finite-time stabilisation for a class of uncertain nonholonomic systems in chained form with output constraint. A nonlinear mapping is first introduced to transform the output-constrained system into a new unconstrained one. Then, by employing the adding a power integrator technique and switching control strategy, a state feedback controller is successfully constructed to render that the states of closed-loop system converge to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of finite-time parking a unicycle-type mobile robot is tackled. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Finite-time stabilisation of a class of stochastic nonlinear systems with dead-zone input

This paper addresses the problem of finite-time stabilisation by state feedback for a class of stochastic nonlinear systems in strict-feedback form. Remarkably, the system under consideration possesses high-order and low-order nonlinear growth rates and the dead-zone input. By delicately combining sign function with adding a power integrator technique, a state feedback controller is designed such that the closed-loop system is finite-time stable in probability. Simulation results of the parallel active suspension system are provided to show the effectiveness of the proposed method.     

Observer and output feedback stabilisation for a class of nonlinear systems

In this paper, we discuss the boundedness of nonlinear stochastic difference systems with time-varying delays. Several criteria on exponential ultimate boundedness in mean square are derived. Examples are also discussed to illustrate the effectiveness of the obtained results.     

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.     

Global stabilisation of the PVTOL aircraft with lateral force coupling and bounded inputs

This work is devoted to prove that the nonlinear control scheme previously proposed by Zavala-Río, Fantoni and Lozano for the global stabilisation of the planar vertical take-off and landing (PVTOL) aircraft with bounded inputs neglecting the lateral force coupling is robust with respect to the parameter characterising such a lateral force coupling, ?, as long as such a parameter takes small enough values. In other words, global stabilisation is achieved even if ? > 0, provided that such a parameter be sufficiently small. As far as the authors are aware, such a property has not been proved in other existing control schemes when the value of ? is not known. The presented methodology is based on the use of embedded saturation functions. Furthermore, experimental results of the control algorithm implemented on a real prototype are presented.     

Local-homogeneity-based global continuous control for mechanical systems with constrained inputs: finite-time and exponential stabilisation

A global continuous control scheme for the finite-time or (local) exponential stabilisation of mechanical systems with constrained inputs is proposed. The approach is formally developed within the theoretical framework of local homogeneity. This has permitted to solve the formulated problem not only guaranteeing input saturation avoidance but also giving a wide range of design flexibility. The proposed scheme is characterised by a saturating-proportional-derivative type term with generalised saturating and locally homogeneous structure that permits multiple design choices on both aspects. The work includes a simulation implementation section where the veracity of the so-cited argument claiming that finite-time stabilisers are faster than asymptotical ones is studied. In particular, a way to carry out the design so as to, indeed, guarantee faster stabilisation through finite-time controllers (beyond their finite-time convergence) is shown.     

Global asymptotic stabilisation of non-linear systems

In this article, the problem of global asymptotic stabilisation of non-linear systems is considered. First of all, the global asymptotic stability of a class of non-linear systems is considered. It is proved that the class of non-linear systems is globally asymptotically stable under certain appropriate conditions. Secondly, based on the result obtained, the global asymptotic stabilisation of a class of non-linear systems is investigated, and the feedback control laws, which globally stabilise the class of systems, are designed. Thirdly, by the coordinate change and the results obtained, the global stabilisation of the affine non-linear systems are studied, and then some sufficient conditions of stabilisation are presented. Finally, the global asymptotic stabilisation of partially linear cascade non-linear system is considered. The sufficient conditions of global stabilisation are obtained, and the corresponding feedback control laws, which stabilise the non-linear systems, are designed. In addition, some examples are given to show the effectiveness of the new results.