Abstract
This paper considers methods for regional robust l2 performance analysis and its state feedback control synthesis of linear time invariant discrete-time systems with saturation nonlinearities via a polytopic approach for the nonlinearities. For the analysis and synthesis, a domain of l2 performance is defined as a domain of initial states guaranteed with l2 performance and exponential stability one. The solvability conditions of the analysis and synthesis problem based on the domain can be recasted as linear matrix inequalities via level sets of quadratic Lyapunov functions, the polytopic approach and constant scaling matrices for the robustness. However, the single state feedback gain without switching cannot achieve non-conservative control performance due to evaluating an admissible set of the exogenous inputs to be large. Specifically, when the exogenous input, the state and the performance output are measurable such as a tracking control problem for servo control systems, this paper proposes a switching control of the state feedback gains designed by the derived synthesis conditions using off-line computation in order to reduce conservativeness of the results without the switching. Finally, this paper verifies effectiveness of our proposed switching control method through a simulation and an experiment.
