Abstract-In this paper a method for robust synthesis of full static-state error feedback and dynamic-output error feedback for master-slave synchronization of Lur'e systems is presented. Parameter mismatch between the systems is considered in the synchronization schemes. Sufficient conditions for uniform synchronization with a bound on the synchronization error are derived, based on a quadratic Lyapunov function. The matrix inequalities from the case without parameter mismatch between the Lur'e systems remain preserved, but an additional robustness criterion must be taken into account. The robustness criterion is based on an uncertainty relation between the synchronization error bound and the parameter mismatch. The robust synthesis method is illustrated on Chua's circuit with the double scroll. One observes that it is possible to synchronize the master-slave systems up to a relatively small error bound, even in the case of different qualitative behavior between the master and the uncontrolled slave system, such as limit cycles and stable equilibria.

Several results on synchronization by Pecora and Carroll [1991], Cuomo and Oppenheim [1993] and Wu and Chua [1994] are evaluated in the context of absolute stability theory, with significant generalizations being achieved. A robustness property of the resulting synchronization criteria is established.

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A method of linear dynamic output feedback for master-slave synchronization of two identical Lur'e systems is introduced. In this scheme, synchronization is obtained using one or at least fewer measurement signals and control signals than the number of state variables of the Lur'e system. A sufficient condition for global asymptotic stability of the error system is derived from a quadratic Lyapunov function and is expressed as a matrix inequality. The dynamic controller is designed by solving a constrained nonlinear optimization problem. The method is demonstrated on Chua's circuit and a hyperchaotic circuit consisting of 2-double scroll cells.

Abstract:In this paper we present a tutorial overview of some of the issues that arise in the design of switched linear control systems. Particular emphasis is given to issues relating to stability and control system realisation. A benchmark regulation problem is then presented. This problem is most naturally solved by means of a switched control design. The challenge to the community is to design a control system that meets the required performance specifications and permits the application of rigorous analysis techniques. A simple design solution is presented and the limitations of currently available analysis techniques are illustrated with reference to this example. Introductory remarksRecent years have witnessed an enormous growth of interest in dynamic systems that are characterised by a mixture of both continuous and discrete dynamics. Such systems are commonly found in engineering practice and are referred to as hybrid or switching systems. The widespread application of such systems is motivated by ever increasing performance requirements, and by the fact that high performance control systems can be realised by switching between relatively simple LTI systems. However, the potential gain of switched systems is offset by the fact that the switching action introduces behaviour in the overall system that is not present in any of the composite subsystems. For example, it can be easily shown that switching between stable sub-systems may lead to instability or chaotic behaviour of the overall system, or that switching between unstable sub-systems may result in a stable overall system. In this paper we present a tutorial introduction to the design of switched linear systems. We begin by discussing how switching arises naturally in many situations. Examples include: the design of control systems for plants that are themselves characterised by switching action (i.e. plants with gears); the design of reconfigurable (fault tolerant) control systems; a switched controller that combines the advantages of several LTI controllers; and using switching to improve the transient response of adaptive control systems. We then discuss the issues in the design of such systems. Of primary practical importance are the issues of asymptotic stability, and issues concerning the realisation of switched linear controllers (and the associated transient response). Each of these issues is illustrated by means of simple illustrative examples.The final part of the paper presents a wind turbine regulation problem. This problem is can be solved using a switched linear controller; the challenge to the community is to design such a controller, while providing theoretical guarantees concerning the issues raised in the paper. A control design is presented which is characterised by a number of switches, and exhibits control performance that is superior to single LTI and non-linear control design. Unfortunately, while this control system works well, both in simulation, and in practice, no guarantees can be given regarding performance and 1 Corresp...