Robust stabilization of nonminimum phase nonlinear systems

The use of avionics networks for flight control system has reduced aircraft weight, system installation, integration and maintenance costs as well as introduced time delays and structured uncertainties. This paper studies the robust stability and stabilisation problem of uncertain networked flight control system with random time delays. Some new sufficient criteria with simple mathematical forms for robust stability and stabilisation of networked flight control system are derived by a free weighting matrix approach. A memoryless state feedback robust controller and the maximum bound of time delay are obtained based on the solution of linear matrix inequalities (LMIs) which are established by the Lyapunov-Krasovskii stability theory. Numerical examples are given to illustrate the effectiveness of design procedure.

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC:15A09, 52A10, 74M05, 93D05.

This paper deals with output feedback stabilisation of a class of nonlinear systems with nonlinearity of the unmeasured state variables. The nonlinearity of the unmeasured state complicates the zero dynamics of the nonlinear system and makes the control design more difficult. In this paper, the zero dynamics analysed for the class of nonlinear systems with respect to the original output and then with respect to a virtual output. It is demonstrated that nonlinear systems with unstable zero dynamics may have stable zero dynamics with the virtual output. Based on the analysis, conditions are then identified for nonlinear systems which can be stabilised by control design with estimated state, including the estimated virtual output, and this removes a restriction of a recent result that requires the transformed system has no zero dynamics. Examples are included to demonstrate that the proposed control design can be used to stabilise nonlinear systems with unstable nonlinear zero dynamics.

This article presents a new approach to robust quadratic stabilization of nonlinear stochastic systems. The linear rate vector of a stochastic system is perturbed by a nonlinear function, and this nonlinear function satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of stochastic systems and, at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable. The new formulation provides a suitable setting for robust stabilization of nonlinear stochastic systems where the underlying deterministic systems satisfy the generalized matching conditions. Our sufficient conditions are written in matrix forms, which are determined by solving linear matrix inequalities (LMIs), which have significant computational advantage over any other existing techniques. Examples are given to demonstrate the results.

Interval Criterion of Robust Stability for Nonlinear System and Its Application to Flight Control

This paper deals with the problem of robust stabilization for linear discrete-time systems under non-linear perturbations. Without limitation to single-input systems and restriction on the structures of both the positive definite matrix and the corresponding variable, a new sufficient condition is presented which guarantees the stability of the closed-loop system and at the same time maximizes the bound on the non-linearity. In addition, our main result is extended to discrete time-delay systems. All the conditions are given within the framework of linear matrix inequalities. The effectiveness of the methods is illustrated with three examples.

The robust stability problem for nonlinear distributed delay stochastic systems with polytopic-type uncertainties is discussed. Based on parameter-dependent Lyapunov-krasovs-kii functional and free-weighting matrix method, a delay-dependent and parameter-dependent stability condition is presented in terms of linear matrix inequalities. The result in this paper improves the existing stability criteria and has less conservativeness. The simulation example shows that the result is effective.

A robust, stabilizing output feedback controller for systems in the normal form, which could potentially include systems with unstable zero dynamics, is presented. The control scheme adopted herein incorporates "smoothed" sliding mode control-chosen for its robustness properties as well as its ability to prescribe or constrain the motion of trajectories in the sliding phase-and an extended high gain observer to estimate one of the unknown functions. Stabilization in the case of an unknown control coefficient and uncertain constant parameters is shown.

Delay-dependent criteria for robust stability and stabilization of fractional-order time-varying delay systems

It is can identify three main classes of problems broadly characterizing stability of a dynamical systems, viz., (1) stability with respect to a part of the variables of the zero equilibrium position (Lyapunov-Rumyantsev stability problem), (2) stability of the partialzero equilibrium position, and (3) stability with respect to a part of the variables of the partialzero equilibrium position. In the problem of stability with respect to a part of the variables of the zero equilibrium position of systems of ordinary differential equations with continuous right-side assumes the domain of initial perturbations to be a sufficiently small neighborhood of the zero equilibrium position. Along with this statement, the case then initial perturbations can be large with respect to one part of non-controlled variables and arbitrary with respect to their other part is also considered. On the other hand, for stability problem of partial zero equilibrium positions of systems of ordinary differential equations also naturally assume that initial perturbations of variables that do not define the given equilibrium position can be large with respect to one part of the variables and arbitrary with respect to their other part. Contrary the assumptions that initial perturbations of this variables are either only arbitrary or only large the combined assumption made it possible an admissible trade-off between the meaning sense for notion of stability and the respective requirements on the Lyapunov functions. The article studies the problem of stability for nonlinear discrete-time systems: stability with respect to a part of the variables of partial equilibrium position. Initial perturbations of variables that do not define the given equilibrium position can be large (belonging to an arbitrary compact set) with respect to one part of the variables and arbitrary with respect to their other part. A conditions of stability of this type are obtained in the context of a discrete analog of the Lyapunov functions method, which generalize a number of existing results. Example is given. The problem of unification of process of studying stability problems of stationary and non-stationary nonlinear discrete-time systems is also discussed

In this paper, the dynamic behavior of reheat power systems is represented by a class of nonlinear time delay models. Both robust stability and state feedback control problems are considered. A convex programming approach is developed to establish tractable conditions expressed by linear matrix inequalities. The effect of finite feedback gains is cast into the analysis. Simulation results of a typical reheat power system are provided to illustrate the theoretical developments.

Due to the existence of dynamical uncertainties, it is important to pay attention to the robustness of nonlinear control systems, especially when designing adaptive critic control strategies. In this paper, based on the neural network learning component, the robust stabilization scheme of nonlinear systems with general uncertainties is developed. Through system transformation and employing adaptive critic technique, the approximate optimal controller of the nominal plant can be applied to accomplish robust stabilization for the original uncertain dynamics. The neural network weight vector is very convenient to initialize by virtue of the improved critic learning formulation. Under the action of the approximate optimal control law, the stability issues for the closed-loop form of nominal and uncertain plants are analyzed, respectively. Simulation illustrations via a typical nonlinear system and a practical power system are included to verify the control performance.

New criteria of almost sure exponential stability and instability of nonlinear stochastic systems with a generalization to stochastic coupled systems

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

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.