# Output feedback based event-triggered sliding mode control for delta operator systems

## TL;DR

This paper introduces a novel output feedback event-triggered sliding mode control method for delta operator systems, addressing issues of numerical ill-conditioning at high sampling rates and ensuring resource-efficient control without Zeno behavior.

## Contribution

It proposes a new multi-rate state estimation technique and integrates it with sliding mode control for delta systems, enhancing stability and efficiency in discrete-time control.

## Key findings

- Effective control demonstrated on a ball and beam system
- Resource-efficient event-triggered control without Zeno phenomenon
- Improved numerical stability at high sampling rates

## Abstract

In this paper, we present an output feedback based design of event-triggered sliding mode control for delta operator systems. For discrete-time systems, multi-rate output sampling based state estimation technique is very useful if the output information is available. But at high sampling rates, the discrete-time representation of the system using shift operator becomes numerically ill-conditioned and as a result, the observability matrix becomes singular as the sampling period tends to zero. Here, a new formulation of multi-rate state estimation (MRSE) for a small sampling period is presented. We first propose a new observability matrix and then discuss its relationship with the observability matrix defined in the conventional sense. For the delta operator system with matched uncertainty, we have presented the design of MRSE based sliding mode control (SMC). Additionally, to make the control efficient in terms of resource utilization, MRSE based event-triggered SMC is proposed. The absence of Zeno phenomenon is guaranteed as the control input is inherently discrete in nature. Finally, the effectiveness of the proposed method is illustrated through numerical simulations, considering a ball and beam system and a general linear system as a numerical example.