The objective of control is to in .uence the behavior of dynamical systems.Achiev- ing fast and accurate control under di .erent environmental conditions,even while assuring stability and robustness,is the aim of all control system design.When environmental changes are signi .cant (e.g.faults o subsystem failures)the design may equire the use of multiple controllers,each of which is appropriate in a speci .c context.By a switching system we mean a hybrid dynamical system with a decision mechanism which orchestrates the switching between di .erent controllers.With great advances in computer technology,and the concomitant increase in the complexity of dynamical systems,switching system are becoming ubiquitous.The analysis and synthesis of such systems is consequently assuming major importance. Stability is the primary equirement of any control system.Once this is assured, optimization of the performance of the overall system can be undertaken within a framework of stability.Following this,modi .cations in the control laws can be un- dertaken to make the system robust under di .erent perturbations.This is the basic philosophy used in conventional control system design as well as in this proposal. Even though research on switching systems has been in progress for many years and numerous contributions have been made to the .eld,basic questions still remain unan- swered.For example the stability of many classes of linear,nonlinear,and adaptive switching systems still remains to be answered,and very little progress has been made in shaping the transient response resulting from the switching action.Both of these important issues are included in the proposal. The proposal consists of three parts.Since stability is undoubtedly the most impor- tant unresolved issue,the .rst part of the proposal is devoted to it.Switching between general linear time-invariant systems and positive linear systems is treated in this con- text.Special attention is given to systems with diagonal Lyapunov functions in view of their importance to switching in decentralized systems.Also treated are piecewise linear systems which are practically important and theoretically tractable.Following this,in the second part of the proposal,the performance that can be achieved by switching is considered.The third and last part of the proposal is devoted to switch- ing in adaptive systems. Intellectual Merit: The PI believes that the research proposed addresses funda- mental questions whose solutions are essential for a better understanding of switching systems.This in turn is vital for the design of future control systems. Broader Impacts: The esearch proposed will enhance collaboration between the PI and other international esearchers (particularly Dr.Robert Shorten at the Hamil- ton Institute,Ireland and Dr.Jens Kalkuhl of Daimler-Chrysler Research),lead to increased interaction with industry,and most important of all,provide training to both graduate and undergraduate students on advanced control techniques. 1
