Finite-time output feedback stabilization of high-order uncertain nonlinear systems

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.     

Input saturation and global stabilization of nonlinear systems viastate and output feedback

For multi-input multi-output nonlinear systems whose free dynamics are Lyapunov stable, the author shows how the problem of global stabilization via dynamic output feedback can be solved by using the technique of input saturation. The power of this technique is also illustrated by solving the problem of global stabilization via bounded state feedback for affine nonlinear systems with stable unforced dynamics. Analogous results are established for discrete-time nonlinear systems     

On global stabilization of a class of nonlinear systems with high-order nonlinearities by state feedback

We consider a problem of global stabilization of a class of nonlinear systems. The considered nonlinear systems are in the approximately feedback linearized form and perturbed nonlinear terms contain high-order terms. We propose a control law that has a dynamic controller gain which is effectively tuned to deal with high-order nonlinear terms. Our new method broadens a class of nonlinear systems under consideration over the existing results.     

Norm estimators and global output feedback stabilization of nonlinear systems WithISS inverse dynamics

A preliminary result on the construction of norm estimators for general nonlinear systems that do not necessarily admit a input output to state stable (IOSS)-Lyapunov characterization is given. Furthermore, an output feedback stabilization scheme is presented that makes use of norm estimators. This construction extends some previous results allowing for more general nonlinearities. Two examples complete the work.     

Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This article further discusses the output feedback stabilization problem for stochastic high-order nonlinear systems with time-varying delay. Under the weaker conditions on nonlinearities in drift and diffusion vector fields, by using the idea of homogeneous domination approach, skillfully choosing an appropriate Lyapunov–Krasoviskii functional, and successfully solving several troublesome obstacles in the design and analysis procedure, an output feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.     

On passivity-based output feedback global stabilization of euler-lagrange systems

It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propggation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.     

Further results on state feedback stabilization of stochastic high-order nonlinear systems

In this paper,a combined homogeneous domination and sign function design approach is presented to state feedback control for a class of stochastic high-order nonlinear systems with time-varying delay.The use of the combined approach relaxes the restriction on nonlinear functions and makes the closed-loop system globally asymptotically stable in probability.     

Losslessness, feedback equivalence, and the global stabilization ofdiscrete-time nonlinear systems

In this paper a necessary and sufficient condition for a nonlinear system of the form Σ, given by x(k+1)=f(x(k))+g(x(k))u(k), y(k)=h(x(k))+J(x(k))u(k), to be lossless is given, and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero-state observable. Then, we investigate conditions under which Σ can be rendered lossless via smooth state feedback. In particular, we show that this is possible if and only if the system in question has relative degree {0,...,0} and has lossless zero dynamics. Under suitable controllability-like rank conditions, we prove that nonlinear systems having relative degree {0,...,0} and lossless zero dynamics can be globally stabilized by smooth state feedback. As a consequence, we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable. The global stabilization problem of the nonlinear system Σ without output is also investigated in this paper by means of feedback equivalence. Some of the results are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear     

A theorem on global stabilization of nonlinear systems by linear feedback

In this paper we investigate the global stabilizability problem for a wide class of single-input nonlinear systems whose the linearization at the equilirrium is controllable. We show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium. The proof of our main theorem is based on some ideas from a previous paper. We use the theorem to recover a recent result of Gauthier et al. concerning the observer design problem.     

Global exponential stabilization of a class of nonlinear systems by output feedback

This work extends the existing output feedback stabilization schemes for the systems in a "perturbed chain-of-integrator" form. In particular, we further relax the triangular-type conditions imposed on the perturbed terms and analyze the robust property of the linear output feedback control law using the newly proposed condition.     

Two results for adaptive output feedback stabilization of nonlinear systems

The problem of (adaptive) stabilization by means of output feedback of a class of nonlinear systems is addressed and solved. The proposed method relies on the asymptotic reconstruction of a stabilizing state feedback control law, does not require stable zero dynamics nor the construction of a Lyapunov function for the closed loop system, and treats in a unified way unknown parameters and unmeasured states. The applicability of the proposed method is discussed via theoretical examples. Finally, it is shown that the proposed method yields a solution to the problem of output feedback regulation for a DC-to-DC power converter and the efficacy of the resulting controller is verified via experiments.     

Practical adaptive output tracking of high-order lower-triangular nonlinear systems: Modular design using feedback domination method

In this paper, a new modular design technique for globally and practically adaptive output tracking of high-order lower-triangular nonlinear systems is proposed. This technique is not based on certainty equivalence principle and completely uses feedback domination method for these linearly parameterized systems. Contrary to the methods based on adding a power integrator technique, for adaptive control of high-order lower-triangular nonlinear systems, in which the choice of a parameter update law is limited to a Lyapunov-type algorithm, the present method does not have this restriction and uses the swapping identifier as its parameter update law. The modularity of designing the controller and the identifier in this method, which relies on control design using feedback domination approach, is completely different from modular design in Immersion and invariance (I&I) based method, which relies on identifier design and desired features of parameter identification. Finally an example illustrates the feasibility and efficiency of the proposed method.     

Passivity, feedback equivalence, and the global stabilization ofminimum phase nonlinear systems

Conditions under which a nonlinear system can be rendered passive via smooth state feedback are derived. It is shown that, as in the case of linear systems, this is possible if and only if the system in question has relative degree one and is weakly minimum phase. It is proven that weakly minimum phase nonlinear systems with relative degree one can be globally asymptotically stabilized by smooth state feedback, provided that suitable controllability-like rank conditions are satisfied. This result incorporates and extends a number of stabilization schemes recently proposed for global asymptotic stabilization of certain classes of nonlinear systems     

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.     

Dynamic output feedback linearization and global stabilization

We present a class of single-input single-output nonlinear systems which are globally transformable by a dynamic output feedback control and a time-varying state space transformation into a linear, observable and minimum phase system. We then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well.     

An iterative solution to dynamic output stabilization and comments on "dynamic output feedback controller design for fuzzy systems".

In this note, we will show that the output feedback controller gains K in the paper is only an approximated solution K* = QP(-1)C0(dagger), with the dagger denoting Moore-Penrose inverse of the matrix C0. Consequently K is not equal to K* and therefore it may not satisfy the linear matrix inequality (LMI) constraints in the aforementioned paper. Instead, an iterative LMI approach is suggested to solve the dynamic output stabilization problem for the fuzzy systems.     

A constructive approach to local stabilization of nonlinear systems by dynamic output feedback

The note considers the problem of local stabilization of nonlinear systems by dynamic output feedback. A new concept, namely, local uniform observability of feedback control law, is introduced. The main result is that if a nonlinear system is Nth-order approximately stabilizable by a locally uniformly observable state feedback, then it is stabilizable by dynamic output feedback. Based on the approximate stability, a constructive method for designing dynamic compensators is presented. The design of the dynamic compensators is beyond the separation principle and can handle systems whose linearization might be uncontrollable and/or unobservable. An example of nonminimum phase nonlinear systems is presented to illustrate the utility of the results.     

Robust interval observers and stabilization design for discrete-time systems with input and output

For a family of nonlinear discrete-time systems with input, output and uncertain terms, a new interval observer is designed. Its main feature is that it is composed of two copies of classical observers. This interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback. An illustrative example completes the presentation.     

Asymptotic output stabilization for nonlinear systems via dynamical variable-structure feedback control

In this article, the problem of asymptotic output stabilization in nonlinear controlled systems is approached from the perspective of dynamical sliding-mode control. The proposed controller is based on Fliess's Generalized Observability Canonical Form, recently derived from the differential algebraic approach to system dynamics.     

Adaptive observers for single output nonlinear systems

An adaptive version of the nonlinear observer obtained by A.J. Krener et al. (1983) is presented. This version involves the cancellation of nonlinear terms by output injection. As an intermediate step, necessary and sufficient conditions are given for transforming a nonlinear system by state-space change of coordinates into the special adaptive observer form that was used by Y. Bastin et al. (1988) to design adaptive observers