We consider continuous time switched systems that are stabilized via a computer. Several factors (sampling, computer computation, communications through a network, etc.) introduce model uncertainties ...produced by unknown varying feedback delays. These uncertainties can lead to instability when they are not taken into account. Our goal is to construct a switched digital control for continuous time switched systems that is robust to the varying feedback delay problem. The main contribution of this note is to show that the control synthesis problem in the context of unknown time varying delays can be expressed as a problem of stabilizability for uncertain systems with polytopic uncertainties
This paper presents a discrete-time model for networked control systems (NCSs) that incorporates all network phenomena: time-varying sampling intervals, packet dropouts and time-varying delays that ...may be both smaller and larger than the sampling interval. Based on this model, constructive LMI conditions for controller synthesis are derived, such that stabilizing state-feedback controllers can be designed. Besides the proposed controller synthesis conditions a comparison is made between the use of parameter-dependent Lyapunov functions and Lyapunov–Krasovskii functions for stability analysis. Several examples illustrate the effectiveness of the developed theory.
This paper is dedicated to the modelling of LTI continuous time systems in digital control loops. We consider the digital control problem on non-uniform sampling periods. Moreover, we assume that ...time varying delays that may have a variation range larger than a sampling period affect the closed-loop. Our goal is to present a unique model that is able to include these problems simultaneously and that can be handled by classical control synthesis tools. We present a new event based discrete-time model (an exponential uncertain system with delay) and we show that the stabilizability of this system can be achieved by finding a control for a switched polytopic system with an additive norm bounded uncertainty. The methodology is extended to the case of switched system.
The stability of discrete-time systems with time varying delay in the state can be analyzed by using a discrete-time extension of the classical Lyapunov–Krasovskii approach. In the networked control ...systems domain a similar delay stability problem is treated using a switched system transformation approach. The paper aims to establish a relation between the switched system transformation approach and the classical Lyapunov–Krasovskii method. It is shown that using the switched systems transformation is equivalent to using a general delay dependent Lyapunov–Krasovskii functionals. This functional represents the most general form that can be obtained using sums of quadratic terms. Necessary and sufficient LMI conditions for the existence of such functionals are presented.
In this paper the sampled-data stabilization of linear time-invariant systems with feedback delay is considered. We assume that the delay is time-varying and that its value is approximatively known. ...We investigate how to use the available information about the evolution of delays for adapting the control law in real time. Numerical methods for the design of a delay-dependent controller are presented. This allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure.
In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. ...Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called "periodic" and "quadratic" protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature.
This article addresses the stability analysis of linear time invariant systems with aperiodic sampled-data control. Adopting a difference inclusion formalism, we show that necessary and sufficient ...stability conditions are given by the existence of discrete-time quasi-quadratic Lyapunov functions. A constructive method for computing such functions is provided from the approximation of the necessary and sufficient conditions. In practice, this leads to sufficient stability criteria under LMI form. The inter-sampling behavior is discussed there: based on differential inclusions, we provide continuous-time methods that use the advantages of the discrete-time approach. The results are illustrated by numerical examples that indicate the improvement with regard to the existing literature.
This paper deals with the study of discrete-time switched affine systems. While generally the literature is focused on the global (practical) stabilization problem, there are classes of switched ...affine systems that can be stabilized only locally. In this paper we deal with such a class of switched affine systems. More precisely, we consider switched affine systems with decoupled switching in the state matrix and the affine input term. For this particular class of systems, a switching control law is designed and conditions ensuring the system local practical stability are provided. A qualitative approach is given based on the existence of a stabilizing linear state feedback. These results are illustrated using a numerical example.
In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals and communication constraints in the sense that, per transmission, ...only one node can access the network and send its information. The order in which nodes send their information is dictated by a network protocol, such as the well-known Round Robin (RR) or Try-Once-Discard (TOD) protocol. Focussing on linear plants and linear continuous-time or discrete-time controllers, we model the NCS with time-varying transmission intervals as a discrete-time switched linear uncertain system. We obtain bounds for the allowable range of transmission intervals in terms of both minimal and maximal allowable transmission intervals. Hereto, a new convex overapproximation of the uncertain switched system is proposed, using a polytopic system with norm-bounded uncertainty, and new stability results for this class of hybrid systems are developed. On the benchmark example of a batch reactor, we explicitly exploit the linearity of the system, leading to a significant reduction in conservatism with respect to the existing approaches.
This paper addresses the Unknown Input Ob-server (UIO) design problem for sampled-data linear time invariant systems with time-varying sampling intervals. A discrete-time modeling approach is used. ...Based on convex optimization techniques, tractable design conditions are proposed and illustrated on a simple model representative of the thermal behavior of a two room house.
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