Stabilizability conditions of multivariable uncertain systems via output feedback control

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

This paper presents the general relative orbit dynamics equations and GPS orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition maintenance of spacecraft formation using GPS code pseudo-ranges are presented. The orbit control of the Earth-Orbiter 1 (EO-1)/Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3D initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.

This paper focuses on the problem of quadratic dissipative control for linear systems with or without uncertainty. We consider the design of feedback controllers to achieve (robust) asymptotic stability and strict quadratic dissipativeness. Both linear static state feedback and dynamic output feedback controllers are considered. First, the equivalence between strict quadratic dissipativeness of linear systems and a H performance is established. Necessary and sufficient conditions for the solution of the quadratic dissipative control problem are then obtained using a linear matrix inequality (LMI) approach. As for uncertain systems, we consider structured uncertainty characterized by a dissipative system. This uncertainty description is quite general and contains commonly used types of uncertainty, such as norm-bounded and positive real uncertainties, as special cases. It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. LMIbased methods for designing robust dissipative controllers are also derived. The results of this paper unify existing results on H and positive real control and provide a more flexible and less conservative robust control design as it allows for a better trade-off between phase and gain performances.

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Decentralized Output Feedback Control of Interconnected Uncertain Delay Systems

This paper considers the problem of output feedback stabilization of multiple time delay uncertain systems with series nonlinearities. We develop a delay-dependent method for designing linear dynamic output feedback controllers which ensures global uniform asymptotic stability for the range of allowable delay times. The proposed stabilization method, which is based on the comparison theorem and some analytical methods, is employed to treat this problem. The most striking feature of the results presented is their simplicity in testing the stabilization of multiple-time-delay systems with series nonlinearities and this can be used to estimate the size of the delay time. Examples are used to illustrate the less conservative results of the proposed methods compared with existing methods in the literature.

This paper presents a method for the design of a controller for rollover prevention using active suspension and an electronic stability program (ESP). Active suspension is designed with linear quadratic static output feedback control methodology to attenuate the effect of lateral acceleration on the roll angle and suspension stroke via control of the suspension stroke and tire deflection of the vehicle. However, this approach has a drawback in the loss of maneuverability because the active suspension for rollover prevention produces in vehicles an extreme over-steer characteristic. To overcome this drawback of the active suspension based method, ESP is designed. Through simulations, the proposed method is shown to be effective in preventing rollover.

This paper proposes the theoretical framework and the consequent application of the input-output Feedback Linearization (FL) control technique to Linear Induction Motors (LIM). LIM, additionally to Rotating Induction Motor (RIM), presents other strong non-linearities caused by the dynamic end effects, leading to a space-vector dynamic model with time-varying inductance and resistance terms and a braking force term. This paper, starting from a recently developed dynamic model of the LIM taking into consideration its end effects, defines a FL technique suited for LIMs, since it inherently considers its dynamic end effects. Additionally, it proposes a technique for the on-line estimation of the inductor resistance, based on Model Reference Adaptive System (MRAS) on-line estimator, exploited for adapting on-line the FL control action versus inductor resistance variations leading to undesirable steady-state tracking errors. The stability of the proposed MRAS on-line estimator has been proven theoretically, adopting the Popov’s criterion for hyperstability. The proposed approach has been validated experimentally on a suitably developed test set-up, under both no load and loaded conditions. It has been compared firstly with the simplest control structure, which is the scalar V/f control, secondly, under the same closed-loop bandwidths of the flux and speed systems, with the industrial standard in terms of high performance control technique: Field Oriented Control (FOC).

This brief deals with the problem of semi-global stabilization by output feedback for a class of uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. In addition, the uncertain nonlinear dynamics of the systems are higher order, rather than linearly growing, in the unmeasurable states. All these make the systems not semi-globally stabilizable by the existing output feedback design schemes. In this brief, by extending the feedback domination design techniques proposed by Qian and Lin, a systematic design scheme is developed to construct linear output feedback controllers that semi-globally stabilize a general class of uncertain nonlinear systems under less restrictive conditions.

This paper addresses the problem of global output feedback stabilization for a class of upper-triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that upper-triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.

This paper considers the problem of robust stabilization of non-minimum phase linear time-invariant single-input single-output uncertain systems. Under certain assumptions, it is shown that non-minimum phase LTI uncertain systems with known order and known and invariant relative degree can be controlled to achieve robust stability by using a linear periodic output feedback controller. The authors' result generalizes similar results for LTI minimum phase uncertain systems. >

This paper is concerned with the problem of global stabilization by output feedback for a class of time-delay nonlinear systems that are dominated by a triangular system satisfying linear growth condition. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF), the linear and memoryless output feedback controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed. An example is given to show that the proposed design procedures are very simple and efficient.

This paper proposes a convex approach to regional stability and ℒ︁2‐gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input‐to‐output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential‐algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ︁2‐gain of the input‐to‐output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full‐order) output feedback controller with a guaranteed bound on the ℒ︁2‐gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is proposed. Given an open-loop, nominal system with information of the uncertainty structure, the proposed robust design method produces a linear constant output feedback control law which maximizes the perturbation bound for maintaining quadratic Lyapunov stability. Both the optimal results for robust analysis and robustness design can be obtained by using an efficient numerical algorithm (e.g. minimax of MATLAB) with analytic gradients given in this paper. Examples are investigated in some detail to show the improvements and advantages of the proposed methods over previous ones.