Matrix Pencil Based On-Line Computation of Controller Parameters in Dynamic High-Gain Scaling Controllers for Strict-Feedback Systems

TL;DR

This paper introduces a matrix pencil based method for designing stabilizing controllers for uncertain nonlinear systems, improving computational efficiency and reducing conservativeness compared to traditional Lyapunov-based approaches.

Contribution

It presents a novel matrix pencil framework for controller design in high-gain scaled systems, capturing system uncertainties more accurately and efficiently.

Findings

Reduced algebraic complexity in controller design

Enhanced feasibility of dual dynamic high-gain control

Validated effectiveness through simulation studies

Abstract

We propose a new matrix pencil based approach for design of state-feedback and output-feedback stabilizing controllers for a general class of uncertain nonlinear strict-feedback-like systems. While the dynamic controller structure is based on the dual dynamic high-gain scaling based approach, we cast the design procedure within a general matrix pencil structure unlike prior results that utilized conservative algebraic bounds of terms arising in Lyapunov inequalities. The design freedoms in the dynamic controller are extracted in terms of generalized eigenvalues associated with matrix pencils formulated to capture the detailed structures (locations of uncertain terms in the system dynamics and their state dependences) of bounds in the Lyapunov analysis. The proposed approach enables efficient computation of non-conservative bounds with reduced algebraic complexity and enhances feasibility of application of the dual dynamic high-gain scaling based control designs. The proposed approach is developed under both the state-feedback and output-feedback cases and the efficacy of the approach is demonstrated through simulation studies on a numerical example.