Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

We study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output feedback controller and prove that the closed-loop system is bounded in probability. Under an infinite-horizon risk-neutral cost criterion, the controller designed can guarantee an arbitrarily small long term average cost. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large, and the risk-neutral cost is guaranteed to be zero. With special care, the controller preserves the equilibrium of the nonlinear system.

SummaryIn this paper, we investigate the problem of global output feedback stabilization for a class of planar nonlinear systems under a more general growth condition, which encompasses both lower‐order and higher‐order state growths with output‐dependent rates. For more accurate estimation, two new observers with nonlinear gains are constructed to estimate the states on the lower‐order and higher‐order scales, respectively. The estimates produced from the dual‐observer are used delicately in the output feedback control law with both lower‐order and higher‐order modes. The overall stability of the system is guaranteed by rigorously choosing these nonlinear gains in the control law and the dual‐observer.

Integral versions of input-to-state stability for dual-rate nonlinear sampled-data systems

This paper investigates the problem of robust output feedback stabilization of uncertain Hamiltonian systems with saturating actuator and input delay. The uncertainties are assumed to be time invariant and belong to convex bounded polytopic domain. By employing Lyapunov-Krasovskii functional method and Wirtinger's inequality, some sufficient conditions are derived for stabilization of nonlinear Hamiltonian systems under consideration. A delay-independent condition in terms of linear matrix inequalities for control of the Hamiltonian systems is established first. And further, an output feedback controller synthesis scheme under the multiple Lyapunov functional framework is proposed which guarantees the robust stability of the closed-loop system when control saturation and delay effectively occur. Finally, numerical results are given to demonstrate the effectiveness of the proposed methodology.

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.

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.

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

The problem of local stabilization of nonlinear control systems with linearizations that contain uncontrollable modes on the imaginary axis is considered. A methodology of designing a stabilizing control is investigated. It involves the following steps: (1) reduction of the stability problem to the stability of the center manifold system, (2) simplification of the vector field on the center manifold using the theory of normal forms, and (3) finding conditions under which the simplified vector field is asymptotically stable. Three cases of degeneracies in the linearized system are treated, and sufficient conditions for the existence of stabilizing controls are given in each case. A theorem is presented regarding the robustness of the above control strategies. >

This paper is concerned with fuzzy-model based stabilization of nonlinear networked control systems (NCSs) with time-varying transmission delays and transmission intervals based on a random-delay approach. The real-time distribution of input delays resulting from transmission delays and intervals is modeled as a dependent and nonidentically distributed process. Then a randomly switched Takagi-Sugeno fuzzy system with multiple input-delay subsystems is proposed to model the nonlinear NCSs. Based on an improved Lyapunov-Krasovskii method, which takes into account the real-time distribution of input delays in estimating cross-product integral terms, new sufficient conditions are deriveed for the exponential stability of the overall systems. The resulting controller design method is equivalent to a nonlinear convex optimization problem with LMI constraints. Numerical examples are presented to substantiate the effectiveness of our results.

The stabilization of two-dimensional non-linear control systems is treated, although the main technique is applicable to more general systems. It combines the theory of centre manifolds and singularities of algebraic functions to design continuous, but not necessarily Lipschitz, stabilizing feedback control laws. In particular, the devices known as the Newton diagram and the Newton or Puiseux polygon are employed to construct uniformizing transformations. Finally, remarks are made about systems for which no continuous stabilizing feedback control law exists.

This correspondence paper addresses the problem of output feedback stabilization of control systems in networked environments with quality-of-service (QoS) constraints. The problem is investigated in discrete-time state space using Lyapunov's stability theory and the linear inequality matrix technique. A new discrete-time modeling approach is developed to describe a networked control system (NCS) with parameter uncertainties and nonideal network QoS. It integrates a network-induced delay, packet dropout, and other network behaviors into a unified framework. With this modeling, an improved stability condition, which is dependent on the lower and upper bounds of the equivalent network-induced delay, is established for the NCS with norm-bounded parameter uncertainties. It is further extended for the output feedback stabilization of the NCS with nonideal QoS. Numerical examples are given to demonstrate the main results of the theoretical development.

This paper addresses an output feedback stabilization problem of a class of nonlinear systems with nonlinearities satisfying the non‐decreasing propertyvialimited‐capacity communication channels. Using ideas from absolute stability theory, we propose an algorithm that consists of an observer and a coder/decoder‐controller pair. Sufficient conditions for the stabilization problem are provided and presented in terms of linear matrix inequalities. Copyright © 2006 John Wiley & Sons, Ltd.

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.

State estimation and stabilization for nonlinear networked control systems with limited capacity channel

The problem of output feedback stabilization of a class of under-actuated benchmark nonlinear systems is discussed. The proposed method utilizes an extended high gain observer (EHGO)-based sliding mode control (SMC) technique to control a class of nonlinear systems which may have unstable zero dynamics. Starting with Lagrangian model of the system and using a suitable coordinate transformation, a generalized normal form representation is derived which decouples the system into an internal and external dynamics. The internal dynamics is utilized to derive an auxiliary system and the full-order EHGO thus obtained is used for estimation of derivative(s) of the system output that are further used in design of an output feedback control law. It is shown that the proposed output feedback controller stabilizes the system and convergence of estimated states is demonstrated with suitable selection of observer parameters. The proposed control scheme is applied to a benchmark nonlinear system, namely inertia wheel pendulum (IWP), in order to demonstrate the efficacy of the technique by simulation.