Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks

In this note, we investigate the stabilization of discrete-time linear systems with an unknown time-varying delay. Existing literature on the stabilization of time-delay systems require some knowledge, such as an upper bound, of the delay. In this paper, by proposing a switched low-gain feedback control law, we are able to achieve asymptotic stabilization of the system without any knowledge of the delay. In addition, the proposed switched low-gain feedback law also significantly improves the closed-loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design. Simulation study illustrates the effectiveness of our theoretical results.

This technical note is concerned with stability of linear discrete-time systems with interval-like time-varying delays. Two new stability criteria are derived by constructing a new Lyapunov functional and utilizing two novel techniques for estimating the forward difference of the Lyapunov functional. The relationship between these stability criteria and some existing ones is established. Through the relationship, it is clear that these stability criteria are less conservative than some existing ones, which is confirmed by a numerical example.

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs between the sensor and controller, and between the controller and actuator. The stabilization of this system is transformed into the robust stabilization of a set of systems. A novel stability result is given for this system, which is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. A synthesis approach of MPC, parameterizing the infinite horizon control moves into a single state feedback law, is proposed. A simulation example is given to illustrate the effectiveness of the proposed MPC.

We study the self-triggered stabilization of discretetime linear systems with quantized state measurements.In the networked control system we consider, sensors may be spatially distributed and be connected to a self-triggering mechanism through finite data-rate channels.Each sensor independently encodes its measurements and sends them to the self-triggering mechanism.The self-triggering mechanism integrates quantized measurement data and then computes sampling times.Assuming that the closedloop system is stable in the absence of quantization and selftriggered sampling, we propose a joint design method of an encoding scheme and a self-triggering mechanism for stabilization.To deal with data inaccuracy due to quantization, the proposed self-triggering mechanism uses not only quantized data but also an upper bound of quantization errors, which is shared with a decoder.

Quantized stabilization of wireless networked control systems with packet losses

This note deals with the delay-dependent stability and stabilization of linear system with state and input delays. Firstly, for the nominal system, by introducing the augmented Lyapunov functional and some free-weighting matrices, new delay-dependent stability and stabilization criteria of the system are presented. Then, these new conditions are extended to handle norm-bounded uncertain systems with state and input delays, which show less conservativeness. Numerical examples are given to illustrate the effectiveness of the proposed results.

In this supplement, we present the stability criterion of Nour-Eldin, based on the Cauchy index and Hankel matrix arguments, and its reduced form, based on reduced Schur-Cohn-Fujiwara criterion. This simplification of the Nour-Eldin criterion is further elaborated by Anderson and Mansour [1991]. A related result, based on reduced Markov stability criterion, was obtained by Mansour and Anderson [1990].

The geometric properties of the canonical parameter space are used to derive necessary conditions for constraining zeros to lie within or on a central circular region of radius α in the z-plane. These necessary conditions are then compared with the sufficient conditions for the stability of linear discrete time systems.

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.

A computationally efficient and simple method is suggested for determining the stability of digital systems. The new method is then compared with other existing methods.

This article concerns the stability and stabilisation of a linear system with both state and input delays. First, the combination of an augmented Lyapunov functional and the free-weighting-matrix technique yields a new delay-independent stability criterion that includes the widely used one as a special case. This criterion is then extended to a new delay-dependent stability criterion by employing an integral inequality. Based on that, a stabilisation approach to design a state feedback controller is presented that requires no parameter tuning, as is needed with some existing methods. Finally, numerical examples illustrate that the method is effective and is an improvement over existing ones.

Stabilization of linear discrete-time systems with actuator saturation

Stabilization of linear discrete-time systems over resource-constrained networks under dynamical multiple description coding scheme

This paper investigates the stabilization problem for discrete-time linear controllable systems subject to actuator saturation. In the case of completely known plants, a control design technique based on a time varying sliding surface is proposed ensuring stabilization under the assumption of availability of all state measurements. Further, in the presence of matched disturbances with known constant bound, a discrete time sliding mode controller is proposed ensuring plant practical stabilization, and a conservative estimate of the attraction domain is given. Theoretical results have been validated by experimental data using a twin-rotor system.

The problem of the local stabilization of linear discrete-time systems subject to bounded controls and suffering from uncertainty of the norm-bounded time-varying type is addressed. From the solution of a certain discrete Riccati equation, a control gain and a set of safe initial conditions are obtained. The asymptotic stability of the saturated closed-loop system is then locally guaranteed for all admissible uncertainties. It is also shown how the control problem can be translated into L.M.I. conditions. The connections between local stability results and disturbance rejection problem are investigated. In the presence of control saturation, it is thus shown that it is possible to reject a certain class of perturbations. Finally, a discretized model of the inverted pendulum allows us to illustrate the results. © 1998 John Wiley & Sons, Ltd.