Proportional-delayed controllers design for LTI-systems: a geometric approach

This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers. © 2017 Informa UK Limited, trading as Taylor %26 Francis Group.

fragility; proportional-delayed controllers; stability; Time-delay systems Closed loop systems; Controllers; Convergence of numerical methods; Decay (organic); Delay control systems; Design; Invariance; Linear systems; Nonlinear control systems; System stability; Time delay; Time varying control systems; Experimental set up; Exponential decay rates; fragility; Geometric approaches; Linear time invariant systems; Nonfragile controllers; Single input single output; Time-delay systems; Linear control systems

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