An improved time-delay implementation of derivative-dependent feedback. (English) Zbl 1406.93265
Summary: We consider an LTI system of relative degree \(r \geq 2\) that can be stabilized using \(r - 1\) output derivatives. The derivatives are approximated by finite differences leading to a time-delayed feedback. We present a new method of designing and analyzing such feedback under continuous-time and sampled measurements. This method admits essentially larger time-delay/sampling period compared to the existing results and, for the first time, allows to use consecutively sampled measurements in the sampled-data case. The main idea is to present the difference between the derivative and its approximation in a convenient integral form. The kernel of this integral is hard to express explicitly but we show that it satisfies certain properties. These properties are employed to construct the Lyapunov-Krasovskii functional that leads to LMI-based stability conditions. If the derivative-dependent control exponentially stabilizes the system, then its time-delayed approximation stabilizes the system with the same decay rate provided the time-delay (for continuous-time measurements) or the sampling period (for sampled measurements) are small enough.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93C57 | Sampled-data control/observation systems |
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