Dissipative stabilization of linear input delay systems via dynamical state feedback controllers: an optimization based approach

TL;DR

This paper introduces a novel dynamical state feedback controller design for stabilizing linear input delay systems with dissipative constraints, using an optimization approach based on bilinear matrix inequalities.

Contribution

It proposes a parameterized dynamical state feedback controller that extends predictor controllers to handle dissipative constraints and input delays effectively.

Findings

The proposed controller stabilizes input delay systems under dissipative constraints.

An inner convex approximation algorithm solves the bilinear matrix inequality efficiently.

Numerical example demonstrates the effectiveness of the proposed method.

Abstract

In this note, we present an effective solution to the stabilization of linear input delay systems subject to dissipative constraints while all the effect of input delay is compensated by a controller with novel structure. The method is inspired by the recent development in the mathematical treatment of distributed delays and predictor controllers, which are critical for the derivation of the solution. An important conceptual innovation is the use of a parameterized dynamical state feedback controller (DSFC), where the dimension of the controller equals the dimension of the control input. A sufficient condition for the existence of a dissipative DSFC is obtained via the Krasovskii functional approach, where the condition includes a bilinear matrix inequality (BMI). To solve the BMI, we apply an inner convex approximation algorithm which can be initialized based on an explicit construction of a predictor controller gain. The proposed DSFC can be considered as an extension of the classical predictor controller, thereby capable of compensating all the effects of the pointwise input delay while satisfying dissipative constraints. A numerical example is given to illustrate the effectiveness of our proposed methodology.