state-space-linearization

Linearize nonlinear dynamics around a reference operating point to obtain A and B matrices.

Updated Jan 15, 2026

Search Tags:#robotics #state-space #linearization #discretization #jacobian #control-design #dynamic-systems

Ready to run

npx skills add https://github.com/KaiserWhoLearns/skillsbench --skill state-space-linearization

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: state-space-linearization
Source: https://github.com/KaiserWhoLearns/skillsbench/tree/main/tasks/r2r-mpc-control/environment/skills/state-space-linearization
Command: npx skills add https://github.com/KaiserWhoLearns/skillsbench --skill state-space-linearization

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

This Skill provides a systematic method to linearize nonlinear dynamics around a chosen operating point, yielding a usable state-space representation for design, analysis, and controller synthesis.

Core Features & Use Cases

Jacobian-based linearization: Compute A and B matrices from the nonlinear dynamics via Jacobians.
Discretization options: Support Euler and matrix-exponential discretization for dt-based implementations.
Use Case: Design a controller for a robotic arm or vehicle by linearizing around the current operating point to simplify control design.

Quick Start

Provide a linearized state-space model around a specified operating point for a given nonlinear system.

Frequently Asked Questions about state-space-linearization

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I linearize nonlinear dynamics for state-space control design?▼

Linearizing nonlinear dynamics requires computing Jacobian matrices around a chosen reference state and input to yield A and B state-space matrices for controller synthesis.

What discretization methods work for continuous-time linearized systems?▼

Euler and matrix-exponential discretization methods are supported for converting continuous-time linearized systems into dt-based discrete versions. This ensures the linearized A and B matrices can be implemented in digital controllers.

When do I need Jacobian-based linearization for a robotic system?▼

You need Jacobian-based linearization when designing a controller for a robotic arm or vehicle by simplifying nonlinear dynamics around the current operating point. It yields a usable state-space representation for analysis and controller synthesis.

Does this state-space linearization approach support R2R control contexts?▼

Yes, the linearization approach supports R2R control contexts by applying appropriate Jacobian and discretization formulas to the nonlinear dynamics. It generates the required state-space matrices for these specific control scenarios.

What prerequisites are needed to compute A and B matrices from nonlinear dynamics?▼

Prerequisites include defining the reference state and input, and performing Jacobian calculations, discretization methods, and stability checks. These steps ensure the resulting linearized state-space model is valid for control design.