Abstract
State feedback synthesis is considered for linear discrete-time systems to minimize an upper bound of the closed-loop induced l 1-norm. A sufficient condition, called Generalized Bounded Real Inequality (GBRI), is presented to establish such a bound. An algorithm similar to the Invariant Kernel Algorithm (Shamma, IEEE Trans. Automat. Control 41 (1996) 533–544) and the contractive set algorithm (Blanchini, IEEE Trans. Automat. Control 39 (1994) 428–433) reduces the analysis and synthesis problems to linear programming. If the problem is feasible, our algorithm gives a polyhedral set that induces a closed-loop Lyapunov function and leads to feasible control laws. An example is given for which the optimal induced l 1-norm achieved by a linear controller is achieved by our synthesis approach.
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