Stabilizability Theorems on Discrete-time Nonlinear Uncertain Systems

TL;DR

This paper establishes new stabilizability theorems for discrete-time nonlinear systems with unknown parameters, showing conditions under which such systems can be stabilized despite complex growth behaviors.

Contribution

It introduces two stabilizability theorems for nonlinear systems with multiple unknown parameters, expanding understanding of stabilization conditions and growth rate implications.

Findings

Stabilizability is achievable if nonlinear growth is polynomially bounded.

Systems can grow exponentially fast yet remain stabilizable.

Discussion on optimality and closed-loop identification enhances control strategies.

Abstract

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule. Later, we find that a stabilizable multi-parameter system in discrete time is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed in this paper.