User Manual for Version 0.2 Introduction Get Started Installation Mathematical Backgrounds Homogeneous Euclidean Space $\mathbb{R}^n_{\mathbf{d}}$ Homogeneous Norm $\|\cdot\|_{\mathbf{ d } }$ Addition $\tilde +$ in Homogeneous Space Multiplication $\tilde \cdot$ in Homogeneous Space Homogeneous Inner Product $\langle \cdot,\cdot\rangle_{\mathbf{ d } }$ Homogeneous Homeomorphism $\Phi$ Inverse Homogeneous Homeomorphism $\Phi^{-1}$ Homogeneous Geometric Objects Homogeneous Curve Homogeneous Sphere Homogeneous Projection Homogeneous Cone Control Design Homogeneous Proportional Control (HPC) Fixed-time HPC Homogeneous Sliding Mode Control (HSMC) Homogeneous Proportional-Integral Control (HPIC) Fixed-time HPIC HSMC with integral action Upgrading Linear Proportional Controller (LPC) to HPC Upgrading Linear Proportional-Integral Controller (LPIC) to HPIC Observer Design Homogeneous Observer (HO) Fixed-time HO Upgrading Linear Observer (LO) to HO Examples Demo of compuation of homogeneous norm Demo of compuation of homogeneous projection Demo of homogeneous algebra Plot of homogeneous curve Plot of homogeneous sphere Plot of homogeneous cone Demo HPC Demo Fixed-time HPC Demo HSMC Demo HPIC Demo Fixed-time HPIC Demo HSMC with integral action Demo Upgrading LPC to HPC Demo Upgrading LPIC to HPIC Demo HO Demo Fixed-time HO Demo Upgrading LO to HO