Brief Optimal induced l1-norm state feedback control

Authors:
Jie Yu;Athanasios Sideris
Affiliations:
Department of Mechanical and Aerospace Engineering, UC Irvine, CA 92697-3975, USA;Department of Mechanical and Aerospace Engineering, UC Irvine, CA 92697-3975, USA
Venue:
Automatica (Journal of IFAC)
Year:
1999

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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.