A new class of finite-time output feedback stabilizers for complex nonlinear systems

The finite-time stabilization for stochastic high-order nonlinear systems is considered in this paper using output feedback. The power orders in the system nonlinearities are relaxed to be rational number greater than one. A new constructive output-feedback, finite-time controller is designed based on a finite-time observer together with the homogeneous domination. The stochastic finite-time stability analysis is given rigorously for the closed-loop stochastic system.

In this paper finite-time stabilization of nonlinear affine systems, is considered. First we provide a formula for a finite-time stabilizing state feedback control law, for the last class of system. Then we extend the result to the case of a norm-bounded uncertain system and a polytopic uncertain system stabilization are given. Some numerical examples are given to illustrate the main result.

Theproblem ofapproximatedecoupling of nonlinear systemsby outputfeedback is considered. The structure of the controller is high-gain proportional plus integral. Linearization of the nonlinear closed-loop equations results in the standard singular perturbation form. Based on the singular perturbation concept, a control law is found that accomplishes approximate decoupling with stability for nonlinear systems. Application oftheproposed design schemeto thefullsix-degree-of-freedomnonlinearaircraftdynamicsmodelispresented,demonstrating itsvalidity. I. Introduction A SYSTEM is said to be decoupled if each component of the output depends only on the corresponding component of the input. The problem of decoupling a multivariable system has been extensively treated in the literature in the past 30 years. The necessary and sufe cient conditions were developed for linear 1;2 and nonlinear 3i6 systems. However, no systematic procedures for the controller design were considered. Nonlinear system controller design is typically approached by linearizing the system about a nominal operating point and applying linear system design methods. This will provide a linear control law that yields approximate noninteracting control and satisfy design objectives in the neighborhood of the constant operating point. For the purpose of this work, the design objectives for this highly coupled system of e ight dynamics are to closely track individual desired outputs, with zero steady-state response from others. However, the problem of computing the decoupling feedback control laws for a nonlinear system is quite dife cult. Approximate decoupling control for nonlinear systems is based onsingularperturbationconcepts.Thestructureofcontrollerishighgain output feedback with proportional plus integral (PI) control.It will be shown that the linearization of nonlinear closed-loop system about the nominal operating point yields the standard singular perturbation equation form when a scalar gain weighting g ! 1. Then,thesingularperturbationconcept,i.e.,necessaryandsufe cient conditions, is utilized to e nd a decoupling control law. This approach is a new, conceptually simple, but practically useful design method for approximate noninteracting control law design with stability for nonlinear systems. The results developed are easy to follow and are easily applicable to aircraft control decoupling problems. This paper introduces the application of this design method to approximate noninteracting e ight control system design.

In this paper we develop a nonsmooth output feedback framework for local and/or global stabilization of a class of inherently nonlinear systems, which may not be achieved by any smooth feedback controller. A systematic design algorithm is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Holder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design procedure, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented fashion. Such nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems with unstabilizable/undetectable linearization. One of them is the global stabilizability of a chain of odd power integrators by Holder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems studied in Qian and Lin (2001), where only global stabilizability by nonsmooth state feedback was proved to be possible.

This paper addresses the issue of finite-time stability (FTS) and finite-time contractive stability (FTCS) of nonlinear systems involving state-dependent delayed impulsive perturbation. Several sufficient conditions are obtained by using theories of impulsive control and Lyapunov stability. The relation between impulsive perturbation and state-dependent delay is established to achieve FTS and FTCS. For time-varying nonlinear system and nonlinear system with fixed parameters, we derive some sufficient conditions based on the main thought of this paper, respectively. Finally, three numerical examples are provided to illustrate the effectiveness and validity of achieved results.

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method

Global stabilization for linear continuous time-varying systems

Design of output feedback semiglobally practically input-to-state (SPIS) stabilizing controllers for nonlinear strict-feedback networked systems is considered. We first design continuous-time state feedback globally asymptotically (GA) stabilizing controllers and discrete-time reduced-order observers and combine the emulation of state feedback controllers and the designed observers to construct discrete-time output feedback controllers. Then we show that the designed controllers SPIS stabilize nonlinear strict-feedback networked control systems when transmission intervals are sufficiently small and communication networks satisfy suitable assumptions. A numerical example is also given to illustrate the efficiency of proposed design of controllers.

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

We consider the problem of finite-time stabilization for nonlinear systems. In the previous work, it was proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system could be achieved by non-Lipschitz continuous state feedback. The proof was based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method proposed in, for the control of nonlinear systems that are impossible to be dealt with by any smooth feedback. A simpler design algorithm is given for the construction of a non-Lipschitz continuous, global finite-time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function that guarantees finite-time stability.

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.

Finite-time output feedback stabilization of lower-triangular nonlinear systems

This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.