Output Feedback Stabilization Of Systems Research Articles

Sampled-data observers for delay systems and hyperbolic PDE–ODE loops

This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be applied to time delay systems of strict-feedback structure, transport Partial Differential Equations (PDEs) with nonlocal terms, and feedback interconnections of Ordinary Differential Equations with a transport PDE. The proposed design approach consists in exploiting any existing observer that features robust exponential convergence of the error when continuous-time output measurements are available. The (continuous-time) observer is then modified, mainly by adding an inter-sample output predictor, to compensate for the effect of data-sampling. Using small-gain analysis, we show that robust exponential stability of the error is preserved, provided the sampling period is not too large. The results are applied to a chemical reactor and to the class of triangular globally Lipschitz delay systems.

Output feedback stabilization for a class of high‐order planar systems with an asymmetric output constraint

SummaryThis article is concerned with the problem of output feedback stabilization for a class of high‐order planar systems with an asymmetric output constraint. By fully extracting the characteristics of system nonlinearities and introducing a delicate manipulation of sign functions, a new tangent‐type asymmetric barrier Lyapunov function and an exquisite nonsmooth observer are proposed. Based on the presented barrier Lyapunov function as well as the nonsmooth observer, the technique of adding a power integrator, that is, a special version of the backstepping design, is skillfully revamped to establish a novel approach which systematically guides us in constructing a continuous output feedback stabilizer and achieving the requirement of a pre‐specified asymmetric output constraint. The developed approach is a unified design in the sense that it is capable of simultaneously performing the output feedback stabilization for systems with and without output constraints, without the need of changing the controller structure. An illustrative example is presented to demonstrate the effectiveness of the proposed strategy.

Sampled-Data Observers for Delay Systems

This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be applied to time delay systems of strict-feedback structure. The proposed design approach consists in exploiting an existing observer, which features robust exponential convergence of the error when continuous-time output measurements are available. The observer is then modified, mainly by adding an inter-sample output predictor, to compensate for the effect of data-sampling. Using Lyapunov stability tools and small-gain analysis, we show that robust exponential stability of the error is preserved, provided the sampling period is not too large.

Static output feedback stabilization for systems with time-varying delay based on a matrix transformation method

This paper is concerned with the problem of static output feedback stabilization for linear systems with time-varying delay. A novel controller design is proposed based on a matrix transformation method with a new equation condition, which can solve the controller gain more easily and avoid complicated calculations of the non-linear matrix inequality. Then, the corresponding criteria can be obtained by combining the matrix transformation method and the ideas of non-uniformly dividing delay interval, which can guarantee the asymptotic stability of the closed-loop systems and calculate the satisfactory controller gain. Finally, two numerical examples are provided to verify the effectiveness of the proposed design scheme.

Dynamic output feedback stabilization for systems with sector-bounded nonlinearities and saturating actuators

In the present work a systematic methodology for computing dynamic output stabilizing feedback control laws for nonlinear systems subject to saturating inputs is presented. In particular, the class of Lur'e type nonlinear systems is considered. Based on absolute stability tools and a modified sector condition to take into account input saturation effects, an LMI framework is proposed to design the controller. Asymptotic as well as input-to-state and input-to-output (in a L2 sense) stabilization problems are addressed both in regional (local) and global contexts. The controller structure is composed of a linear part, an anti-windup loop and a term associated to the output of the dynamic nonlinearity. Convex optimization problems are proposed to compute the controller considering different optimization criteria. A numerical example illustrates the potentialities of the methodology.

Stability and output feedback stabilization for systems with Markovian switching and impulse effects

We investigate the exponential stability in the mean square sense for the systems with Markovian switching and impulse effects. Based on the statistic property of the Markov process, a stability criterion is established. Then, by the parameterizations via a family of auxiliary matrices, the dynamical output feedback controller can be solved via an LMI approach, which makes the closed-loop system exponentially stable. A numerical example is given to demonstrate the method.

Output feedback stabilization for systems presenting sector-bounded nonlinearities and saturating inputs

In the present work a systematic methodology for computing output stabilizing feedback control laws for nonlinear systems subject to saturating inputs is presented. In particular, the class of L'ure type nonlinear systems is considered. Based on absolute stability tools and a modified sector condition to take into account input saturation effects, an LMI framework is proposed to design the controller. Both regional (local) and global stabilization results are presented. The controller structure is composed by a linear part, an anti-windup loop and a term associated to the output of the dynamic nonlinearity. Convex optimization problems are proposed in order to compute the controller matrices aiming at the maximization of the basin of attraction, or the performance enhancement with a guaranteed region of stability. A numerical example illustrates the potentialities of the methodology.

SOME RESULTS ON ROBUST OUTPUT FEEDBACK STABILIZATION OF NONLINEAR SYSTEMS1

This paper aims at extending the results presented in (Teel and Praly, 1995) about the design of output feedback stabilizers for systems in normal form starting from Uniformly Completely Observable (UCO) state feedback control laws in two main directions: first, we show how output feedback asymptotic stabilization can be achieved even without requiring local exponential stability of the state feedback UCO-based loop and without designing an explicit local nonlinear observer. Second, we show how to design the output feedback stabilizer starting from an UCO state feedback control law which is not vanishing on the desired asymptotic attractor which, as a consequence, may be not invariant for the original controlled system. Key tools in achieving this goal are the ones developed in (Marconi et al., 2006) in a context strongly inspired by output regulation problems.

On Static Output Feedback Stabilization of Systems With Stable Generalized Zero Dynamics

In this note, we define generalized zero dynamics, introduce a generalized zero dynamics algorithm, and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback.

Output Feedback Stabilization of Systems with Uncertainty

We consider output feedback stabilization for an uncertain controlled system of a high relative order. The proposed approach reduces the relative order of the system by structural dynamic adjustment of the controlled plant. Sufficient adjustment conditions are stated in the form of a “functional relationship” and a control algorithm ensuring these conditions in a feedback system is proposed.

Output feedback stabilization of systems with non-linear actuators

An output feedback controller is developed to provide stabilization for feedback-linearizable systems with asymptotically-stable non-linear actuators. The controller consists of a globally-bounded state feedback and a high-gain observer. It is established that if the actuator dynamics are sufficiently fast, then the developed output feedback controller will stabilize the origin of the closed-loop system regardless of how fast the observer is. A simulation example is included to illustrate the developed theory.

On output feedback stabilization of Euler-Lagrange systems with nondissipative forces

This paper provides a solution to the problem of output feedback stabilization of systems described by Euler-Lagrange equations perturbed by nondissipative forces. This class of forces appears in some applications where we must take into account the interaction of the system with its environment. The nonlinear dependence on the unmeasurable part of the state and the loss of the fundamental passivity property render most of the existing results on stabilization of nonlinear systems unapplicable to this problem. The technique we use consists of finding a dynamic output feedback controller and a nonlinear change of coordinates such that the closed loop can be decomposed as a cascade of an asymptotically stable system and an input-to-state stable system. This should be contrasted with the well-known passivity-based technique that aims at a feedback interconnection of passive systems. We believe this design methodology to be of potential applicability to other stabilization problems where passivity arguments are unapplicable.