1. S-Plane Poles & System Matrix A
Drag poles on s-plane (s = σ + jω)
Discretization Method
Ā = exp(A·Δ)
Step Size Δ (Sampling Interval)
0.10 s
Mamba Selective Gating Δ(t)
Enabled
Eigenvalues λ(A)
-1.200 ± 2.500i
Discrete Matrix Ā
[[0.858, 0.217], ...]
Discrete Vector B̄
[[0.093], [0.042]]
System Output C
[1.000, 0.000]
Continuous to Discrete Math: Continuous ODE
dx/dt = Ax + Bu transforms via Laplace to transfer function H(s) = C(sI - A)⁻¹B. Discrete recurrence x_k = Ā x_{k-1} + B̄ u_k uses ZOH matrix exponential Ā = e^(A·Δ).
2. Recurrent vs Convolutional Duality & Signal Response
Global Parallel Convolution y = u * k vs Step-by-Step Recurrence
Discrete System Step Response y_k vs Time t
Sequence Length N = 64
3. Context Scaling: SSM vs Transformer Attention
Computational Complexity & State Memory Efficiency
State Space Model (Mamba) O(N) Time / O(1) State
0.06 ms
Parallel Scan Convolution during training; Recurrent O(1) state buffer during inference. Sequence N=64.
Transformer (Attention) O(N²) Time / O(N) Cache
4.10 ms
Full Softmax Attention Matrix N×N KV-Cache grows quadratically with sequence length.
Sequence Context Length N
64 tokens