# Mixed Control Strategy for a Class of Sector-Bounded Nonlinear Systems

## TL;DR

This paper introduces a mixed control strategy combining deterministic and stochastic elements to manage nonlinear systems more effectively.

## Contribution

The novel approach integrates white noise into control gain, offering advantages in systems requiring precise control signal mean and variance.

## Key findings

- Mixed control strategy outperforms deterministic control in managing nonlinear systems.
- Matrix Inequalities conditions ensure stability and performance in closed-loop systems.
- Numerical examples demonstrate the effectiveness of the mixed control approach.

## Abstract

Here, mixed-strategy-based control of systems with sector-bounded nonlinearities is considered. The suggested control strategy applies a stochastic state feedback, where the control gain includes a white noise component in addition to the deterministic part. While each of the control signal components can sometimes accomplish the control task independently, the combination may have some merits. This is especially true when both the mean value and the variance of the control signal need to be quantified separately. Systems that apply deterministic state-feedback control are abundant, whereas the application of state-multiplicative noise as a mean of control is more limited. Nevertheless, Stochastic Anti Resonance (SAR) with state-multiplicative noise based control, are encountered in diverse engineering applications, physics modelling, and biological models, such as visual-motor tasks. Matrix Inequalities conditions are derived, for weighted L2-gain using a mixed strategy control along with exponential LP-stability of the closed-loop. A numerical example is given, where the merit of mixed control strategy comparing to deterministic control is demonstrated.