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SUMMARYThis paper presents new finite-dimensional linear matrix inequality formulations for several important analysis problems of linear parameter-varying systems. The approach is based on a non-smooth dissipative systems framework using a continuous, piecewise-affine parameter-dependent Lyapunov function. The new analysis approach yields guaranteed and less conservative results than previously published techniques that are based on affine parameter-dependent Lyapunov functions or Lur! e e-Postnikov Lyapunov functions. Conservatism is reduced in this new approach because the analysis uses a more general class of parameterdependent Lyapunov functions (PDLFs). The new approach also provides an explicit trade-off between conservatism and computational effort of the analysis technique. Note that, in contrast to the gridding approach typically used to develop a computationally feasible algorithm, this proposed approach guarantees the analysis results. This paper also shows that the numerical results of our approach, while computationally intensive, could be used to develop many new insights into the selection of PDLFs in the other analysis techniques.

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This paper investigates a new design technique of input shaping filters for multi-input flexible systems using convex optimization synthesis techniques for finite impulse response filters (FIR filters). The objective of the input shaping filter design is to find the minimum length and the minimum number of nonzero impulses of the FIR filter that forces the system to track the reference command without any residual vibration, while satisfying additional performance and control constraints. This multi-objective optimization is solved using a two-step algorithm that sequentially solves two quasi-convex optimization problems. Compared with previously published nonlinear optimization approaches, this new approach does not require a priori knowledge of the forms of input shaping filters and enables much greater flexibility for including additional performance and robustness objectives. Furthermore, this convex-based approach can be applied to multi-input systems. The multiple input shaping filter has been experimentally verified on the Stanford University Two-Link Flexible Manipulator.

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