Uncertain Discrete-time Systems Research Articles

A new approach to design set-membership state estimators for discrete-time linear systems based on the observability matrix

The paper introduces a method for synthesising set-valued state estimators for uncertain discrete-time linear systems. Based on the past values of the input and output of the system and on its observability matrix, a non-conservative numerical scheme is proposed to characterise at each time instant a tight enclosure of the actual state vector of the system. Interval analysis and consistency techniques are applied to design this guaranteed state estimator. In addition, the finite-time convergence of the width of the estimated state enclosures is shown. A comparison study, with some existing methods in the literature, throughout numerical examples is presented.

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

This paper considers the simultaneous stabilization problem which concerns finding a single controller to simultaneously stabilize a finite collection of discrete-time nonlinear systems with time-varying state delay and norm-bounded uncertainties. For this purpose, a simultaneously stabilizing discrete-time sliding mode controller (DT-SMC) is synthesized. Based on the delay-dependent Lyapunov–Krasovskii functional method, sufficient conditions are derived which guarantee the existence of a common sliding surface in terms of a nonconvex feasibility problem. The cone complementarity linearization approach is exploited to transform the nonconvex conditions into a convex optimization problem. Finally, the robust simultaneously stabilizing DT-SMC is designed in order to draw the closed-loop trajectories of each system onto the common sliding surface in finite time and to maintain it thereafter. The effectiveness of the proposed method is investigated by simulation of a practical example.

An Improved Approach to Robust $$H_\infty $$ Filtering for Uncertain Discrete-Time Systems with Multiple Delays

This paper is concerned with the robust $$H_\infty $$ filtering problem for a class of discrete-time systems with polytopic uncertainties and multiple time delays. Different from the most existing techniques, the novel augmented Lyapunov–Krasovskii functionals are constructed by incorporating the relationships between multiple time delays. Based on the proposed functionals and the Wirtinger-based inequality, sufficient conditions are first established under which the filtering error system is asymptotically stable and has an prescribed $$H_\infty $$ performance level. Then, the adjusting parameters are introduced such that the filter gains can be effectively obtained by solving certain linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness and the benefit of the proposed approach.

Discrete-Time Sliding Mode Control for Deployment of Tethered Space Robot With Only Length and Angle Measurement

This paper proposes a nonlinear discrete-time sliding mode based tension control for deployment of tethered space robot with only length and angle measurements. The discrete-time dynamics of deployment is uncovered based on discretization of Hamilton's principle. Taking into account the underactuated dynamics, the proposed discrete-time sliding surface can generate a specified reduced-order system, which can be regarded as an uncertain discrete-time system with multiple time delays, which is caused by a considerable sample interval, and the stability of a reduced-order system is well analyzed by combining a linear matrix inequation technique based on robust control theory and nonlinear discrete-time Lyapunov method. A novel input structure with the auxiliary variable sequence is presented to deal with the tension saturation, and the states can converge to the specified reduced-order system although the input saturation occurs. The proposed discrete-time method makes no appeal to velocity terms. It is cost-effective to use the proposed method for the information of length and angle are easily measured rather than that of velocity, and it conduces to low requirements for the measurement ability of sensors. Simulation results verify the stability analyses, and are coincident with the stability analyses.

Fuzzy-Model-Based Output Feedback Sliding-Mode Control for Discrete-Time Uncertain Nonlinear Systems

This paper addresses the output feedback sliding-mode control (SMC) problem for discrete-time uncertain nonlinear systems through Takagi-Sugeno fuzzy dynamic models. Combining with the sliding surface, a descriptor system is constructed to characterize the sliding motion dynamics. Sufficient conditions for asymptotic stability analysis of the sliding motion are attained by the piecewise quadratic Lyapunov functions within a convex optimization setup. Two SMC design approaches are proposed to ensure the finite-time convergence of the sliding surface. Two simulation examples are presented to show the effectiveness of the proposed approaches.

Robust output regulation of discrete-time linear systems by quantized output feedback control

This technical communique studies the robust output regulation problem of uncertain discrete-time linear systems by quantized output feedback control. We show that, under the same assumptions as those that guarantee the solvability of the robust output regulation problem by a dynamic output feedback control law, our problem is also solvable by a dynamic quantized output feedback control law as long as the quantization density is greater than certain explicitly specified lower bound.

Robust Guaranteed Cost Control Under Digital Communication Channels

This paper investigates the feedback guaranteed cost control problem for a class of uncertain discrete-time systems with input quantization. The plant with polytope type uncertainties is considered. The input signal will be quantized by a dynamic quantizer before it is transmitted from the controller to the system under digital communication channels. First, a design method of the feedback control for the quantized closed-loop system is given to attain the same guaranteed cost performance as the one without signal quantization. Then, by introducing some useful auxiliary scalars, the dynamic parameter of the quantizer is also designed effectively so that the desired performance level can be achieved. A simulation example is provided to show the effectiveness of the proposed design method.

On $H_\infty$ Sliding Mode Control Under Stochastic Communication Protocol

This paper is concerned with the sliding mode control (SMC) problem for a class of uncertain discrete-time systems subject to unmatched external disturbances and communication constraints. In order to reduce the bandwidth usage between the controller and the actuators, the stochastic communication protocol (SCP) is utilized to determine which actuator should be given the access to the network at a certain instant. A key issue of the addressed problem is to design both the sliding surface and the sliding mode controller under the SCP scheduling. An updating rule on actuator input is first introduced and then a token-dependent SMC law is designed. Sufficient conditions are established for the resultant SMC systems such that not only the reachability with a sliding domain around the specified sliding surface is ensured, but also the stochastic stability with a prescribed $H_\infty$ performance level is guaranteed. Based on these conditions, a set of coupled matrix inequalities is given to acquire the token-dependent parameter matrices in the proposed SMC law. Finally, a numerical example is presented to illustrate the effectiveness of the proposed $H_\infty$ SMC scheme under the SCP scheduling.

Resilient $$H_{\infty }$$ H ∞ Filtering for Stochastic Systems with Randomly Occurring Gain Variations, Nonlinearities and Channel Fadings

In this paper, the resilient $$H_{\infty }$$ filtering problem for a class of stochastically uncertain discrete-time systems with randomly occurring gain variations, nonlinearities (RONs) and channel fadings is investigated. Considering the existences of random parameter fluctuations in both actual plant and filter, a sequence of mutually independent random variables with known probabilistic distribution is utilized to better describe the stochastic characteristics. The phenomenon RONs, which is regulated by random variables with Bernoulli distribution, is used to reflect the reality that actual systems are generally nonlinear. The system measurement with channel fadings is described by the stochastic Rice fading model, where the channel coefficients are a set of mutually independent random variables with any probability density function. It is worthwhile to mention that a series of slack matrix variables are exploited to eliminate the coupling between the plant matrices and the designed filter parameters by providing free dimensions in the solution space. The purpose of this paper is to design a resilient $$H_{\infty }$$ filter such that the filtering error system is asymptotically stable with a prescribed $$H_{\infty }$$ performance level. And sufficient conditions for filter design are eventually converted into solving a convex optimization problem over linear matrix inequalities. A numerical example is presented to illustrate effectiveness of the proposed approach.

Design of static output-feedback controller for uncertain discrete time systems with positivity constraint on closed-loop system and control signal

Design of static output-feedback controller for uncertain discrete time systems with positivity constraint on closed-loop system and control signal

Event-triggered Control With Self-triggered Sampling for Discrete-time Uncertain Systems

This paper proposes a resource-aware control approach for discrete-time linear uncertain systems. The approach uses a self-trigger condition to determine the sampling time to guarantee that the system is uniformly ultimately bounded and an event-trigger condition to determine control updates. The self-trigger condition is constructed using the skewed structured singular value to treat uncertainties in the prediction, and the event-trigger condition is constructed by considering the costs of sampling and control updates. A numerical example is provided to illustrate the approach.

Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances

In this paper, we study the robust observer design and observer-based control design problems for a class of discrete one-sided Lipschitz systems subject to uncertainties and disturbances. The nonlinearities are assumed to be one-sided Lipschitz and quadratically inner-bounded. By utilizing a new approach which is an extension of the H∞ filtering method, our robust observer design can relax some limitations in existing works. In order to derive design conditions in terms of linear matrix inequalities, several mathematical techniques are appropriately used to linearize the bilinear terms which unavoidably emerge in observer and observer-based control designs for discrete-time uncertain systems. Via a numerical example, we show that while existing works fail, our results work effectively.

Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

Optimal linear filtering for networked control systems with time-correlated fading channels

In this paper, the problem of filtering for discrete-time networked control systems with time-correlated fading channels is considered where each time-correlated fading channel is described by a one-dimensional discrete-time uncertain linear system model with random disturbance. Using the innovation analysis approach and optimal estimates for the products of channel gain and system state obtained, an optimal linear recursive filter is proposed, that has time-independent complexity, and does not increase computation and storage load with time. An example and simulation are provided to show the effectiveness and potential of the proposed new design technique.

Networked iterative learning control for systems with packet dropout and communication delay

In this paper, we consider networked iterative learning control (NILC) design for a class of uncertain discrete-time nonlinear systems with random packet dropout and communication delay, where the input-output coupling parameter (IOCP) is assumed to be unknown. Firstly, we present a learning scheme for the unknown IOCP. Then a simple NILC scheme is developed. It is strictly proved that under certain conditions the developed scheme can guarantee zero-error convergence. Finally, an example is given to validate the findings.

Is it Possible to Stabilize Discrete-Time Parameterized Uncertain Systems Growing Exponentially Fast?

This paper derives a somewhat surprising but interesting result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to intuition, it shows that the nonlinear growth ra...

Multi-Power Reaching Law Based Discrete-Time Sliding-Mode Control

This paper proposes a multi-power reaching law-based sliding-mode control (SMC) for uncertain discrete-time systems. The proposed controller mainly consists of the multi-power function along with the perturbation estimation. Different from the existing similar works, the control gains of the controller are adaptively adjusted by the multi-power function, i.e., three power terms, according to different stages of the convergence process. Hence, the system trajectory of the controlled system can be forced toward the sliding surface with a faster convergence rate. The corresponding sliding-mode dynamics and the reaching steps to the sliding surface are theoretically analyzed. A practical example is given to examining the validity of the proposed method. The simulation results show that the proposed method reduces the reaching steps while guaranteeing better control accuracy than the single power method.

Computational method for estimating the domain of attraction of discrete-time uncertain rational systems

Using linear matrix inequality (LMI) conditions, we propose a computational method to generate Lyapunov functions and to estimate the domain of attraction (DOA) of uncertain nonlinear (rational) discrete-time systems. The presented method is a discrete-time extension of the approach first presented in [39], where the authors used Finsler’s lemma and affine annihilators to give sufficient LMI conditions for stability. The system representation required for DOA computation is generated systematically by using the linear fractional transformation (LFT). Then a model simplification step not affecting the computed Lyapunov function (LF) is executed on the obtained linear fractional representation (LFR). The LF is computed in a general quadratic form of a state and parameter dependent vector of rational functions, which are generated from the obtained LFR model. The proposed method is compared to the numeric n-dimensional order reduction technique proposed in [11]. Finally, additional tuning knobs are proposed to obtain more degrees of freedom in the LMI conditions. The method is illustrated on two benchmark examples.

Observer-Based Finite-Time Nonfragile Control for Nonlinear Systems With Actuator Saturation

This paper considers a design problem of dissipative and observer-based finite-time nonfragile control for a class of uncertain discrete-time system with time-varying delay, nonlinearities, external disturbances, and actuator saturation. In particular, in this work, it is assumed that the nonlinearities satisfy Lipschitz condition for obtaining the required results. By choosing a suitable Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained in terms of linear matrix inequalities, which ensures the finite-time boundedness and dissipativeness of the resulting closed-loop system. Meanwhile, the solvability condition for the observer-based finite-time nonfragile control is also established, in which the control gain can be computed by solving a set of matrix inequalities. Finally, a numerical example based on the electric-hydraulic system is provided to illustrate the applicability of the developed control design technique.

Mean square consensus of uncertain discrete-time stochastic multi-agent systems with x-dependent noise

ABSTRACTIn this paper, the mean square consensus control problem is investigated for linear uncertain discrete-time multi-agent systems with x-dependent noise and time-varying delays. Under undirected connected topology, the robust consensus problem of multi-agent systems is converted into the robust stabilisation problem for the discrete-time stochastic systems. By utilising Lyapunov functional and the linear matrix inequality method, some new sufficient conditions are derived to guarantee the consensus of uncertain discrete-time stochastic multi-agent systems. Based on the state feedback controller protocol with time-varying delays, a new consensus criterion is established for the discrete-time stochastic multi-agent systems with parameter uncertainties. Finally, numerical examples are provided to illustrate the effectiveness of the proposed results.