Positive-realness analysis of sampled-data systems and its applications

In this paper, we first study strong positive-realness of sampled-data systems and introduce a measure called positive-realness gap index. We show that this index can be computed efficiently with a bisection method, and provide state space formulas for its computation. The importance of this index lies in that it is useful for robust stability analysis of sampled-data systems. An iterative procedure for computing an exact robust stability margin is given and illustrated through a numerical example.     

Randomized algorithms for quadratic stability of quantized sampled-data systems

In this paper, we present a novel development of randomized algorithms for quadratic stability analysis of sampled-data systems with memoryless quantizers. The specific randomized algorithm employed generates a quadratic Lyapunov function and leads to realistic bounds on the performance of such systems. A key feature of this method is that the characteristics of quantizers are exploited to make the algorithm computationally efficient.     

Absolute stability analysis of linear systems with Duhem hysteresis operator

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input–output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.     

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.     

Stability of sampled-data piecewise affine systems: A time-delay approach

This paper addresses the stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is first considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampled-data closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficient conditions for non-fragility of the stabilizing continuous-time PWA state feedback controller. The results are successfully applied to a helicopter example.     

Controller designs for bilateral teleoperation with input saturation

Input saturation raises a stability issue in a bilateral teleoperation system when a master robot whose motion is induced by a human operator moves fast in abnormal situation and a slave robot cannot follow the motion command due to the input saturation. In this paper, we conduct rigorous stability analyses of the teleoperation system under the input saturation. We first extend analysis of teleoperation scheme proposed in Chopra and Spong (2004) to a case of the input saturation, in which analysis is valid for a local operation region whose size is dependent on the input capacity. We further develop a new control scheme that guarantees the stability for a global operation region. Therefore, the proposed control scheme can deal with extreme cases, e.g., the speed of motion of the master robot can be substantially greater than the actuator capability of the slave robot. Simulations and experiments are subsequently conducted to verify the effectiveness of the analyses.     

Absolute stability of sampled-data systems with a sector nonlinearity

This paper studies the absolute stability problem of sampled-data systems with a sector nonlinearity. Using the FR-operator technique, a frequency-domain criterion with a Nyquist-like plot is derived. It can be regarded as a sampled-data version of the circle criterion. It is shown that the “absolute-stability gain margin” can be read directly from the plot.     

Norm invariant discretization for sampled-data fault detection

In this paper, the problem of fault detection in sampled-data systems is studied. It is shown that norms of a sampled system are equal to the corresponding norms of a certain discrete time system. Based on this discretization, the sampled-data fault detection problem can be converted to an equivalent discrete-time problem. A framework that unifies the H₂ and H_∞ optimal residual generators in sampled-data systems is then proposed.     

Digital versus analog control of bilateral teleoperation systems: A task performance comparison

Controller discretization has the potential to jeopardize the stability of a bilateral teleoperation system. As reported in the literature, stability conditions impose bounds on the gains of the discrete-time controller and the sampling period and also a trade-off between the two. This paper shows a choice of task for which large sampling periods, necessitating low control gains for maintaining stability, lead to low teleoperation transparency and unacceptable task performance. It continues to show that users can successfully perform the same task if the controller is implemented using analog components. This highlights the advantages of analog haptics in tasks involving the display of highly stiff environments. The paper also highlights the constraints in designing analog haptic teleoperation controllers and proposes design guidelines to address them.     

Minimum-phase criterion on sampling time for sampled-data interval systems using genetic algorithms

In this paper, a genetic algorithm-based approach is proposed to determine a desired sampling-time range which guarantees minimum phase behaviour for the sampled-data system of an interval plant preceded by a zero-order hold (ZOH). Based on a worst-case analysis, the identification problem of the sampling-time range is first formulated as an optimization problem, which is subsequently solved under a GA-based framework incorporating two genetic algorithms. The first genetic algorithm searches both the uncertain plant parameters and sampling time to dynamically reduce the search range for locating the desired sampling-time boundaries based on verification results from the second genetic algorithm. As a result, the desired sampling-time range ensuring minimum phase behaviour of the sampled-data interval system can be evolutionarily obtained. Because of the time-consuming process that genetic algorithms generally exhibit, particularly the problem nature which requires undertaking a large number of evolution cycles, parallel computation for the proposed genetic algorithm is therefore proposed to accelerate the derivation process. Illustrated examples in this paper have demonstrated that the proposed GA-based approach is capable of accurately locating the boundaries of the desired sampling-time range.     

A novel approach for stability and transparency control of nonlinear bilateral teleoperation system with time delays

In this paper, a novel control approach is presented to improve the stability and transparency of the nonlinear bilateral teleoperation system with time delays, where a four-channel (4-CH) architecture using modified wave reflection reduction transformation is explored in order to guarantee the passivity of the communication channels in the nonlinear bilateral teleoperation system; a sliding-mode controller is proposed to compensate for the dynamic uncertainties and enhance the system synchronization performance in finite time. The system stability has been analyzed using Lyapunov functions. The proposed method is validated through experimental work based on a 3-DOF bilateral teleoperation platform in the presence of time delays. The experimental results clearly demonstrate that the proposed control algorithm has superiority on system transparency over other wave-based systems.     

Polynomial-time probabilistic observability analysis of sampled-data piecewise affine systems

This paper proposes a polynomial-time probabilistic approach to solve the observability problem of sampled-data piecewise affine systems. First, an algebraic characterization for the system to be observable is derived. Next, based on the characterization, we propose a randomized algorithm that can determine if the system is observable in a probabilistic sense or the system is not observable in a deterministic sense. Finally, it is shown with some examples, for which it is hopeless to check the observability in a deterministic way, that the proposed algorithm is very useful.     

Conic sectors for sampled-data feedback systems

A multivariable analog system can be controlled by a sampled-data compensator. A conic sector that can be used to analyze the closed-loop stability and robustness of this feedback system is presented in this letter.     

Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.     

Control of sampled-data systems with variable sampling rate

This paper addresses stability and performance of sampled-data systems with variable sampling rate, where the change between sampling rates is decided by a scheduler. A motivational example is presented, where a stable continuous time system is controlled with two sampling rates. It is shown that the resulting system could be unstable when the sampling changes between these two rates, although each individual closed-loop system is stable under the designed controller that minimizes the same continuous loss function. Two solutions are presented in this paper. The first solution is to impose restrictions on switching sequences such that only stable sequences are chosen. The second solution presented is more general, where a piecewise constant state feedback control law is designed which guarantees stability for all possible variations of sampling rate. Furthermore, the performance defined by a continuous time quadratic cost function for the sampled-data system with variable sampling rate can be optimized using the proposed synthesis method.     

A novel adaptive robust control architecture for bilateral teleoperation systems under time‐varying delays

Bilateral teleoperation technology has caused wide attentions due to its applications in various remote operation systems. The communication delay becomes one of the main challenging issues in the teleoperation control design. Meanwhile, various nonlinearities, parameter variations, and modeling uncertainties existing in manipulator and environment dynamics need to be considered carefully in order to achieve good control performance. In this paper, a globally stable nonlinear adaptive robust control algorithm is developed for bilateral teleoperation systems to deal with these control issues. Namely, the unknown dynamical parameters of the environmental force are estimated online by the improved least square adaptation law. A novel communication structure is proposed where only the master position signal is transmitted to the slave side for the tracking design, and the online estimators of the environmental parameters are transmitted from the slave to the master to replace the traditional environmental force measurement. Because the estimated environmental parameters are not power signals, the passivity problem of the communication channel and the trade‐off limitation between the transparency performance and robust stability in traditional teleoperation control are essentially avoided. The nonlinear adaptive robust control is subsequently developed to deal with nonlinearities, unknown parameters, and modeling uncertainties of the master, slave, and environmental dynamics, so that the guaranteed transient and steady‐state transparency performance can be achieved. The experiments on two voice‐coil motor‐driven manipulators are carried out, and the comparative results verify that the proposed control algorithm achieves the excellent control performance and the guaranteed robust stability simultaneously under time delays. Copyright © 2014 John Wiley & Sons, Ltd.     

PD-like controller for delayed bilateral teleoperation of wheeled robots

This paper proposes a proportional derivative (PD)-like controller applied to the delayed bilateral teleoperation of wheeled robots with force feedback in face of asymmetric and varying-time delays. In contrast to bilateral teleoperation of manipulator robots, in these systems, there is a mismatch between the models of the master and slave (mobile robot), problem that is approached in this work, where the system stability is analysed. From this study, it is possible to infer the control parameters, depending on the time delay, necessary to assure stability. Finally, the performance of the delayed teleoperation system is evaluated through tests where a human operator drives a 3D simulator as well as a mobile robot for pushing objects.     

Finite-time stability of linear time-varying systems with jumps

This paper deals with the finite-time stability problem for continuous-time linear time-varying systems with finite jumps. This class of systems arises in many practical applications and includes, as particular cases, impulsive systems and sampled-data control systems. The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential-difference linear matrix inequalities. The sufficient condition turns out to be more efficient from the computational point of view. Some examples illustrate the effectiveness of the proposed approach.     

New conic sectors for sampled-data feedback systems

New conic sectors are presented which can be used to analyze sampled-data feedback systems. First, a cone is constructed which contains just the sampler. Next, by using conic sector results for interconnected systems, the cone is propagated to the entire sampled-data operator. The new cone result is less conservative (has a smaller radius) and removes the restriction of an open-loop stable sampled-data compensator.     

Absolute exponential stability and stabilization of switched nonlinear systems

This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings.