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Sliding Mode Control of Discrete-Time Switched Systems with Repeated Scalar Nonlinearities

机译：具有重复标量非线性的离散时间切换系统的滑模控制

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摘要

This note studies the design of sliding mode control (SMC) for discrete-time hybrid stochastic switched systems with repeated scalar nonlinearities. The weighed ℋ gain performance is considered for the system dynamics to optimize its transient state performance. First, sufficient conditions are given to guarantee the corresponding system is exponentially stable while achieving a desired weighed ℋ performance. A new switching surface function is constructed by the average dwell time technique and the positive diagonally dominant Lyapunov functional method to further reduce the conservativeness induced by the repeated scalar nonlinearity. Then, the corresponding sliding mode dynamics are obtained and the solvability condition for the desired switching surface function is derived. Furthermore, the synthesis of the proposed SMC law is proposed to force the resulting closed-loop system trajectories onto the pre-specified sliding mode region with a desired level of accuracy. Finally, the feasibility and the effectiveness of the presented new design techniques are illustrated by examples and simulations.
机译：本文研究具有重复标量非线性的离散时间混合随机切换系统的滑模控制（SMC）设计。系统动态考虑了加权后的增益性能，以优化其瞬态性能。首先，给出足够的条件以确保相应的系统在达到理想的称重性能的同时呈指数稳定。通过平均停留时间技术和正对角占优Lyapunov函数方法构造了一个新的开关表面函数，以进一步降低由重复标量非线性引起的保守性。然后，获得相应的滑模动力学，并得出所需开关表面函数的可溶性条件。此外，提出了所提出的SMC定律的综合，以期望的精确度将所得的闭环系统轨迹强制到预定的滑模区域上。最后，通过实例和仿真说明了所提出的新设计技术的可行性和有效性。

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