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2. State-space representation - Wikipedia

   en.wikipedia.org/wiki/State-space_representation

   Stability and natural response characteristics of a continuous-time LTI system (i.e., linear with matrices that are constant with respect to time) can be studied from the eigenvalues of the matrix . The stability of a time-invariant state-space model can be determined by looking at the system's transfer function in factored form.

3. Metzler matrix - Wikipedia

   en.wikipedia.org/wiki/Metzler_matrix

   The exponential of a Metzler (or quasipositive) matrix is a nonnegative matrix because of the corresponding property for the exponential of a nonnegative matrix. This is natural, once one observes that the generator matrices of continuous-time Markov chains are always Metzler matrices, and that probability distributions are always non-negative.

4. Stability theory - Wikipedia

   en.wikipedia.org/wiki/Stability_theory

   If all eigenvalues of J are real or complex numbers with absolute value strictly less than 1 then a is a stable fixed point; if at least one of them has absolute value strictly greater than 1 then a is unstable. Just as for n =1, the case of the largest absolute value being 1 needs to be investigated further — the Jacobian matrix test is ...

5. Exponential stability - Wikipedia

   en.wikipedia.org/wiki/Exponential_stability

   An exponentially stable LTI system is one that will not "blow up" (i.e., give an unbounded output) when given a finite input or non-zero initial condition. Moreover, if the system is given a fixed, finite input (i.e., a step ), then any resulting oscillations in the output will decay at an exponential rate , and the output will tend ...

6. Nyquist stability criterion - Wikipedia

   en.wikipedia.org/wiki/Nyquist_stability_criterion

   The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...

7. The best digital photo frames of 2025 - AOL

   www.aol.com/lifestyle/best-digital-photo-frames...

   Aspect ratio: Although most modern phones can snap 1:1 (square) or 16:9 (wide) photos, the default setting tends to be 4:3. Some frames, however, have 16:9 screens, meaning you'll end up with ...