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L2-gain of double integrators with saturation nonlinearity Goncalves, Jorge in IEEE Transactions on Automatic Control (2002), 47(12), 2063-2068 This note uses quadratic surface Lyapunov functions (SuLFs) to efficiently check if a double integrator in feedback with a saturation nonlinearity has L -gain less than > 0. We show that for many such ... [more ▼] This note uses quadratic surface Lyapunov functions (SuLFs) to efficiently check if a double integrator in feedback with a saturation nonlinearity has L -gain less than > 0. We show that for many such systems, the L -gain is nonconservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of 1. These results allow the use of classical analysis tools like -analysis or integral quadratic constraints to analyze systems with double integrators and saturations, including servo systems like some mechanical systems, satellites, hard disks, compact disk players, etc. [less ▲] Detailed reference viewed: 76 (0 UL)The Introduction of a Design Heuristics Extraction Method ; Blessing, Lucienne ; in Advanced Engineering Informatics (2002), 16 Detailed reference viewed: 43 (1 UL)Quadratic Surface Lyapunov Functions in the Analysis of Feedback Systems with Double Integrators and Saturations Goncalves, Jorge in Proceedings of the 10th IEEE Mediterranean Conference on Control and Automation (2002) Many systems like servo systems, satellites, harddisks, and CD players, can be modeled as linear systems with a single integrator and a saturation. Many times, such systems are controlled with a PI ... [more ▼] Many systems like servo systems, satellites, harddisks, and CD players, can be modeled as linear systems with a single integrator and a saturation. Many times, such systems are controlled with a PI controller resulting in a feedback interconnection with a double integrator and a saturation. In this paper, we propose a loop transformation that results in bounded operators so that classical analysis tools like mu-analysis or IQCs can be applied. In order to show boundedness of all operators, we use quadratic surface Lyapunov functions to efficiently check if a double integrator in feedback with a saturation nonlinearity has L2 -gain less than gamma > 0 . We show that for many of such systems, the L2 -gain is non-conservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of . [less ▲] Detailed reference viewed: 46 (0 UL)L2-gain of double integrators with saturation nonlinearity Goncalves, Jorge in Proceedings of the 15th IFAC World Congress (2002) This paper uses quadratic surface Lyapunov functions to efficiently check if a double integrator in feedback with a saturation nonlinearity has L2-gain less than gamma > 0. We show that for many of such ... [more ▼] This paper uses quadratic surface Lyapunov functions to efficiently check if a double integrator in feedback with a saturation nonlinearity has L2-gain less than gamma > 0. We show that for many of such systems, the L2-gain is non-conservative in the sense that they are approximately equal to the low erbound obtained by replacing the saturation with a constant gain of 1. These results allow the use of classical analysis tools like mu -analysis or IQCs to analyze systems with double integrators and saturations, including servo systems like some mechanical systems, satellites, hard-disks, CD players, etc. [less ▲] Detailed reference viewed: 49 (1 UL) |
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