Linear parameter-varying state-delay (LPVSD) systems: stability and L2-gain controllers

Authors:
Magdi S. Mahmoud;Naser F. Al-Muthairi
Affiliations:
College of Engineering, UAE University, PO Box 17555 Al-Ain, UAE and Faculty of Engineering, Arab Academy for Sciences and Technology, PO Box 2033, Al-Horryia, Helliopolis-Cairo, Egypt;College of Engineering, UAE University, PO Box 17555 Al-Ain, UAE and Department of Electrical Engineering, Kuwait University, PO Box 5969, Safat-13060, Kuwait
Venue:
Systems Analysis Modelling Simulation
Year:
2003

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Abstract

In this article, we investigate a class of linear parameter-varying state-delay (LPVSD) systems where the state-space matrices depend on time-varying parameters and the time-delay is unknown but bounded. We treat both notions of quadratic stability (using a single quadratic Lyapunov-Krasovskii function) and affine quadratic stability (using parameter-dependent Lyapunov-Krasovskii functions). In both cases, we develop LMI-based delay-independent and delay-dependent conditions for stability testing. Then, we design state-feedback controllers which guarantee quadratic stability and an induced L2-norm bound. For the case of dynamic output feedback control, we use a parameter-independent quadratic Lyapunov-Krasovskii function to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set.