STABILIZATION OF A CLASS OF NONLINEAR NON‐MINIMUM PHASE SYSTEMS

This paper tackles the problem of stabilization of a class of non‐minimum phase nonlinear systems which have zero dynamics with an eigenvalue zero of multiplicity 2. By adding some new terms, called cross terms, we are able to generalize the concept of the Lyapunov function with a homogeneous derivative along the trajectory, which was introduced in [4], to produce a suitable Lyapunov function. The Lyapunov function assures that the stability of an approximate system, which consists of some lower order terms of a nonlinear system with an eigenvalue zero of multiplicity 2, implies the stability of the whole system. Applying these to non‐minimum phase zero dynamics of nonlinear systems with such a center, a sufficient condition and a design method of state feedback control are obtained for stabilizing the systems.     

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

A controller that stabilizes second‐order vector systems in predefined‐time is introduced in this paper. That is, for second‐order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller that first drive the system trajectories to a linear manifold in predefined time and then drives the system trajectories to a non‐smooth manifold with the predefined‐time stability property, in predefined time also; this is done in order to avoid the differentiability problem that inherently appears when stabilizing high‐order systems in finite time under the block control principle technique. The proposal is applied to the predefined‐time exact tracking of fully actuated mechanical systems. As an example, the proposed solution is applied to a two‐link planar manipulator, and numerical simulations are conducted to show its performance.     

Modified performance of MIMO wireless networked time‐delay systems over fading channels

In this paper, the modified performance limitation of multi‐input multi‐output (MIMO) wireless networked time‐delay systems over fading channels is investigated, where the characteristic of the fading channels is assumed to be a random process. The modified tracking performance limitation is considered based on frequency domain representation. The display expressions of performance limitation are achieved by using the co‐prime factorization and the spectral decomposition techniques. The obtained results show that the modified performance limitation of the wireless networked time‐delay systems is related to the inherent characteristics of the given plant, including the non‐minimum phase zeroes, the unstable poles, the encoding‐decoding, the fading channels, the bandwidth and the modified factor. Finally, some numerical examples are provided to demonstrate the efficiency of the proposed design method.     

STABILITY ANALYSIS OF UNCERTAIN DISCRETE‐TIME SYSTEMS WITH TIME‐VARYING STATE DELAY: A PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH

This paper presents several new robust stability conditions for linear discrete‐time systems with polytopic parameter uncertainties and time‐varying delay in the state. These stability criteria, derived by defining parameter‐dependent Lyapunov functions, are not only dependent on the maximum and minimum delay bounds, but also dependent on uncertain parameters in the sense that different Lyapunov functions are used for the entire uncertainty domain. It is established, theoretically, that these robust stability criteria for the nominal and constant‐delay case encompass some existing result as their special case. The delay‐dependent and parameter‐dependent nature of these results guarantees the proposed robust stability criteria to be potentially less conservative.     

Performance Limitation of Networked Systems with Network‐Induced Delay and Packet‐Dropout Constraints

In this paper, we deeply investigate the tracking performance limitation of single‐input single‐output (SISO) networked systems with packet dropouts and network‐induced delay constrains, where the power of the tracking error is adopted to measure of the performance and is minimized by searching through all stabilizing one‐parameter controllers, with/without considering the channel input power. Moreover, the explicit expressions of the tracking performance limitation are obtained by applying the spectral factorization technique. Theoretical analysis shows that the tracking performance limitation is closely dependent on non‐minimum phase zeros, unstable poles of a given plant, the characteristics of the reference signals, network‐induced delay and packet dropouts probability of communication channel. Finally, some typical examples and simulations are conducted to illustrate the theoretical results.     

Finite‐Time Stability of Linear Caputo‐Katugampola Fractional‐Order Time Delay Systems

In this paper, a finite‐time stability procedure is suggested for a class of Caputo‐Katugampola fractional‐order time delay systems. Sufficient conditions are derived to prove this fact. Numerical results are provided to demonstrate the validity of our theoretical results.     

Reachable set estimation for discrete‐time linear systems with time delays

This paper is concerned with the reachable set estimation problem for discrete‐time linear systems with multiple constant delays and bounded peak inputs. The objective is to check whether there exists a bounded set that contains all the system states under zero initial conditions. First, delay‐dependent conditions for the solvability of the addressed problem are derived by employing a novel Lyapunov–Krasovskii functional. The obtained conditions are expressed in terms of matrix inequalities, which are linear when only one scalar variable is fixed. On the basis of these conditions, an ellipsoid containing the reachable set of the considered system is obtained. An approach for determining the smallest ellipsoid is also provided. Second, the approach and results developed in the first stage are generalized to the case of systems with polytopic parameter uncertainties, and delay‐dependent conditions are given in the form of relaxed matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

A new tracking controller for discrete‐time SISO non minimum phase systems

A new tracking controller for discrete‐time Single Input Single Output (SISO) non‐minimum phase (NMP) systems is presented. In the proposed method, after cancelation of poles and cancelable zeros of the system, the controller adds some NMP zeros to compensate the effect of NMP zero (zeros) of the system. As a result, the phase of the overall transfer function will be almost linear and its magnitude approaches unity for all frequencies. The method can be applied even to the systems with complex conjugate NMP zeros. As well, it is applicable to the systems for which the conventional methods cannot properly be used. Furthermore, a generalization of method to continuous‐time systems is another given result. Several examples are provided to illustrate the effectiveness of the method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Precise Tracking for Continuous‐Time Non‐Minimum Phase Systems

Stable inversion based precise tracking for continuous‐time square or nonsquare non‐minimum phase systems is studied. However, high precision trajectory tracking of non‐minimum phase systems can be obtained by the stable inversion method but requiring large enough extended time interval. In order to solve this problem of large extended time restriction, a novel approach to precise trajectory tracking of non‐minimum phase systems is proposed, it is called the improved stable inversion (ISI) method, using an optimal integration of the pre‐actuation and the optimal state transition (OST) techniques. The ISI method can obtain precise trajectory tracking with a smaller extended time interval as compared to the stable inversion method. The proposed method achieves better validation through numerical simulations for the non‐minimum phase system.     

Optimal transient performance under output set‐point reset

The purpose of this paper is to propose a new method for the optimization of the output transition in the case of set‐point reset for LTI, non‐minimum phase, possibly non‐hyperbolic plants. Assuming that the plant is stabilized by a proper feedback controller, the problem consists in finding a feedforward linear filter yielding a suitable reference trajectory for the closed‐loop system. The approach situates in the framework of model pseudo‐inversion because the external reference trajectory is computed starting from some desired features of the transient output between the two set points. A significant aspect of the new method is that the transition trajectory is not ‘ad hoc’ exactly prespecified by the designer. Rather, it is implicitly defined by the procedure for the minimization of a suitable multi‐objective quadratic cost functional. As no pre‐actuation is required, the method can be practically implemented on line and also works for the critical class of non‐hyperbolic systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Observer‐based Fault Estimators Using Iterative Learning Scheme for Linear Time‐delay Systems with Intermittent Faults

This paper deals with the fault estimation problem for a class of linear time‐delay systems with intermittent fault and measurement noise. Different from existing observer‐based fault estimation schemes, in the proposed design, an iterative learning observer is constructed by using the integrated errors composed of state predictive error and tracking error in the previous iteration. First of all, Lyapunov function including the information of time delay is proposed to guarantee the convergence of system output. Subsequently, a novel fault estimation law based on iterative learning scheme is presented to estimate the size and shape of various fault signals. Upon system output convergence analysis, we proposed an optimal function to select appropriate learning gain matrixes such that tracking error converges to zero, simultaneously to ensure the robustness of the proposed iterative learning observer which is influenced by measurement noise. Note that, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality (LMI) by the Schur complements and Young relation. In addition, the results are both suit for the systems with time‐varying delay and the systems with constant delay. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods and two comparability examples are provided to prove the superiority of the algorithm.     

Robust H∞ Control for Non‐Minimum Phase Switched Cascade Systems with Time Delay

The H_∞ control of a class of the uncertain switched nonlinear cascaded systems with time delay is explored in this paper via the multiple Lyapunov functions. The considered systems are assumed to comprise an inherently nonlinear and a linearizable nonlinear dynamic system that may be non‐minimum phase. A group of partial differential inequalities containing adjustable functions are used in the control design task. The state feedback controllers and a suitable switching law are designed simultaneously so as to achieve the desired disturbance attenuation while preserving asymptotic stability for all admissible uncertainties. The partial differential inequalities are of lower dimension than general Hamilton–Jacobi inequalities, and therefore the solving process is feasible. This particular technique is applicable even if no subsystem is asymptotically stable. The non‐minimum phase property is compensated for by means of an appropriate switching mechanism. A robust H_∞ control for non‐switched cascade system with time delay is obtained in addition. An illustrative example is given to demonstrate the efficiency of the proposed design method.     

An improved non‐sequential multi‐input multi‐output quantitative feedback theory design methodology

This paper presents an improved non‐sequential multi‐input multi‐output (MIMO) Quantitative Feedback Theory (QFT) design methodology for uncertain systems. A non‐sequential MIMO QFT stability theorem is derived that serves as the basis for an improvement of the design methodology, whereby it can be successfully applied to non‐minimum phase systems, albeit with a degree of conservatism partially inherent in independent and decentralized design methodologies. The results reduce the conservatism in a non‐sequential MIMO QFT design and provide insight into the plant cases for which the methodology can be successfully applied. Copyright © 2006 John Wiley & Sons, Ltd.     

On multiple‐delay output feedback stabilization of LTI plants

We develop a control methodology for linear time‐invariant plants that uses multiple delayed observations in feedback. Using the special coordinate basis, we show that multiple‐delay controllers can always be designed to stabilize minimum‐phase plants, and identify a class of non‐minimum‐phase plants that can be stabilized using these controllers. Copyright © 2009 John Wiley & Sons, Ltd.     

Compensation of time‐varying input delay for discrete‐time nonlinear systems

We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.     

Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Discrete‐time low‐gain control strategies are presented for tracking of constant reference signals for finite‐dimensional, discrete‐time, power‐stable, single‐input, single‐output, linear systems subject to a globally Lipschitz, non‐decreasing input nonlinearity and a locally Lipschitz, non‐decreasing, affinely sector‐bounded output nonlinearity (the conditions on the output nonlinearities may be relaxed if the input nonlinearity is bounded). Both non‐adaptive and adaptive gain sequences are considered. In particular, it is shown that applying error feedback using a discrete‐time ‘integral’ controller ensures asymptotic tracking of constant reference signals, provided that (a) the steady‐state gain of the linear part of the plant is positive, (b) the positive gain sequence is ultimately sufficiently small and (c) the reference value is feasible in a very natural sense. The classes of input and output nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone. The discrete‐time results are applied in the development of sampled‐data low‐gain control strategies for finite‐dimensional, continuous‐ time, exponentially stable, linear systems with input and output nonlinearities. Copyright © 2001 John Wiley & Sons, Ltd.     

Time‐varying linear controllers for exponential tracking of non‐holonomic systems in chained form

In this paper, the authors address the tracking problem for non‐holonomic systems in chained form with target signals that may exponentially decay to zero. By introducing a time‐varying co‐ordinate transformation and using the cascade‐design approach, smooth time‐varying controllers are constructed, which render the tracking‐error dynamics globally ??‐exponentially stable. The result shows that the popular condition of persistent excitation or not converging to zero for the reference signals is not necessary even for the globally ??‐exponential tracking of the chained‐form system. The effectiveness of the proposed controller is validated by simulation of two benchmark mechanical systems under non‐holonomic constraints. Copyright © 2006 John Wiley & Sons, Ltd.     

Combined inverse and gradient iterative learning control: performance,monotonicity, robustness and non‐minimum‐phase zeros

Based on recent papers that have demonstrated that robust iterative learning control can be based on parameter optimization using either the inverse plant or gradient concepts, this paper presents a unification of these ideas for discrete‐time systems that not only retains the convergence properties and the robustness properties derived in previous papers but also permits the inclusion of filters in the input update formula and a detailed analysis of the effect of non‐minimum‐phase dynamics on algorithm performance in terms of a ‘plateauing’ or ‘flat‐lining’ effect in the error norm evolution. Although the analysis is in the time domain, the robustness conditions are expressed as frequency domain inequalities. The special case of a version of the inverse algorithm that can be used to construct a robust stable anti‐causal inverse non‐minimum‐phase plant is presented and analysed in detail. Copyright © 2012 John Wiley & Sons, Ltd.     

Consensus of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises

This paper studies the consensus problem of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises. Directed switching topologies are considered. Firstly, for a kind of switching topology with each digraph containing a spanning tree, we give a weak consensus result on the basis of the mode‐dependent average dwell time method. Then, if all digraphs in a switching topology are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue, we prove that the mean square and almost sure consensus can always be guaranteed for an arbitrary switching sequence with some constant distributed control gains, and we also give the statistic properties of the final consensus points. Numerical examples are presented to illustrate the effectiveness of our results. Copyright © 2017 John Wiley & Sons, Ltd.