This paper investigates the design of guaranteed cost controllers for a class of linear systems with a state delay using a time-multiplied linear quadratic cost function. Based on delay-dependent and delay-independent stability criteria, guaranteed cost controllers can be constructed via solutions to linear matrix inequalities (LMIs) such that the resulting closed-loop system is stable and a specified time-multiplied linear integral-quadratic cost function has an upper bound. By the cone complementary linearization method, delay-dependent state feedback controllers can be derived in terms of LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.
Time-Multiplied Guaranteed Cost Control of Linear Delay Systems
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Wang, J., Lam, J., Xu, S., and Shu, Z. (September 25, 2008). "Time-Multiplied Guaranteed Cost Control of Linear Delay Systems." ASME. J. Dyn. Sys., Meas., Control. November 2008; 130(6): 061007. https://doi.org/10.1115/1.2977473
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