# Feedback Passivation of Linear Systems with Fixed-Structured Controllers

## TL;DR

This paper develops a method to design optimal fixed-structured output feedback controllers for linear systems, maximizing passivity levels in both continuous and discrete time, using convex optimization.

## Contribution

It provides necessary and sufficient conditions for passivation with fixed-structured controllers and formulates the controller design as a convex optimization problem.

## Key findings

- Conditions for passivation with fixed-structure controllers are established.
- The method maximizes passivity indices via convex optimization.
- Applicable to both continuous-time and discrete-time systems.

## Abstract

This paper addresses the problem of designing an optimal output feedback controller with a specified controller structure for linear time-invariant (LTI) systems to maximize the passivity level for the closed-loop system, in both continuous-time (CT) and discrete-time (DT). Specifically, the set of controllers under consideration is linearly parameterized with constrained parameters. Both input feedforward passivity (IFP) and output feedback passivity (OFP) indices are used to capture the level of passivity. Given a set of stabilizing controllers, a necessary and sufficient condition is proposed for the existence of such fixed-structured output feedback controllers that can passivate the closed-loop system. Moreover, it is shown that the condition can be used to obtain the controller that maximizes the IFP or the OFP index by solving a convex optimization problem.