Being a unique phenomenon in hybrid systems, mode switchis of fundamental importance in dynamic and control analysis. Inthis paper, we focus on global long-time switching and stabilityproperties of conewise linear systems (CLSs), which are a class oflinear hybrid systems subject to state-triggered switchingsrecently introduced for modeling piecewise linear systems. Byexploiting the conic subdivision structure, the “simple switchingbehavior” of the CLSs is proved. The infinite-time mode switchingbehavior of the CLSs is shown to be critically dependent on twoattracting cones associated with each mode; fundamental propertiesof such cones are investigated. Verifiable necessary andsufficient conditions are derived for the CLSs with infinite modeswitches. Switch-free CLSs are also characterized by exploringthe polyhedral structure and the global dynamical properties. Theequivalence of asymptotic and exponential stability of the CLSs isestablished via the uniform asymptotic stability of the CLSs thatin turn is proved by the continuous solution dependence on initialconditions. Finally, necessary and sufficient stability conditionsare obtained for switch-free CLSs.

The paper addresses the robust adaptive control problem of robot manipulators. The dynamic equations of robot manipulators and their fundamental properties that facilitate analysis and control system design are first reviewed. Then the direct, indirect, and combined direct and indirect adaptive control approaches of robot manipulators are presented. After that, a number of variable structure adaptive control approaches which combines features of the robust design based on variable structure systems with parameter adaptive control, are studied. After that, a new combined adaptive and variable structure adaptive control approach is proposed for the tracking control of robot manipulators under the uncertainty environment. This is a robust, high-performance adaptive control scheme that combines the advantages and overcomes the disadvantages of both types of techniques. Finally, the extensive comparing simulation results are presented to demonstrate the theory study.