For questions about steady states in systems theory, which are unchanging in time.

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LQR definitions

I have to define the choice of parameters I have chosen to create an LQR controller for a drone, and I have written the following: High penalties in the Q matrix mean that the state will try to ...
10 views

Markov chain converges to the same steady state for different initial probability vectors.

I was asked to write a code to simulate the following Markov chain, and find the PMF of the random variable $X$: The code I've written for simulating the given Markov chain: ...
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Are these steady states of non linear dynamic system actually steady states?

I have the following non linear dynamic system in discrete time: x_{t+1} = \frac{1}{1 + \exp\left(- \beta \left( 2 d \left(c + \frac{(1 - c)}{1 + a (1 - x_{t}) d}\right) - b - d \...
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How to solve the Ordinary differential equation with denominator having functional variable

How to solve the Second order Ordinary differential equation with denominator having functional variable x''(y)+x'(y)-(x(y)-z(y))/(x(y)+z(y))=0
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Exsitence of stationary distribution for M/M/1 with non-homogeneous poisson arrival rate

Consider an M/M/1 queue where arrivals occur at rate $\lambda(t)$ according to a Poisson process at time $t$ and move the process from state $i$ to $i+1$, and service times have an exponential ...
• 462
1 vote
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Periodic Summation Response. How to separate its Transient and Steady-State Expression?

Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ...
• 151
1 vote
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Regarding an equation in an iteration method

I am going through a paper on an iterative method related to discrete optimal regulator, G. Hewer, "An iterative technique for the computation of the steady state gains for the discrete optimal ...
• 113
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Terminology for stability of equilibria in systems with discrete state-space

What is the proper terminology to describe the stability of a fixed point in a system with a discrete state-space? The states compose a high dimensional discrete torus, and the fixed point in question ...
1 vote
54 views

Fixed point versus point with slope $0$

When solving a first order differential equation $$\frac{dy}{dx} = f(y)$$ for the fixed points (or steady states), we set the differential equation to $0$ and solve for the values of $y$ that are ...
1 vote
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Sequential dynamical system

I would like to understand the following example based on the following definition Definition: Alternatively, one can choose to update the states of the variables according to some fixed update order, ...
• 4,708
I have been looking at the following equations in an article* and wanted to know how the $E(∞)$ was derived. By substituting $\gamma E$ for $A$ and factorising it is easy to see how $E(∞)$ can equal 0 ...