Control of impulsive renewal systems: Application to direct design in networked control

— We consider the control of impulsive systems with jumps triggered by a renewal process, that is, the intervals between jumps are independent and identically distributed. The control action and output measurement are assumed to take place only at jump times. Necessary and sufficient conditions, in the form of LMIs, are given for mean square stabilizability and detectability for the class of systems considered. An infinite horizon quadratic optimal control problem is solved, under appropriate stabilizability and detectability properties. The class of impulsive renewal systems is shown to be especially suited to model networked control systems utilizing CSMA-type protocols, with stochastic intervals between transmissions and packet drops. In this setting, the analysis and synthesis tools mentioned above are used to (i) prove that for an emulationbased design, stability of the closed-loop is preserved if the distribution of the intervals between transmissions assigns high probability...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Duarte Antunes, João Pedro Hespanha, Carlos Jorge Ferreira Silvestre
• Keywords: CDC 2009, Control Systems, Impulsive Systems, Mean Square Stabilizability, Quadratic Optimal Control