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Post Closed as "Needs details or clarity" by Marco Golla, user1688, Stefan Kohl♦, ofer zeitouni, Noah Stein
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Ed Tate
Ed Tate
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Given a discrete-time linear time-varying system (LTV)

$$x(k+1) = A(k) x(k) + B(k) u(k)$$

where $A(k)$ and $B(k)$ are generated by a stationary random process. Is there an equivalent linear time-invariant (LTI) system which will calculate the expected trajectory of $x(k)$?

$$\mathbb E[x(k+1)] = z(k+1) = A_{\text{eq}} z(k) + B_{\text{eq}} u(k)$$

If so, how is it calculated?

If not, are there conditions where this can be calculated?

Given a discrete-time linear time-varying system (LTV)

$$x(k+1) = A(k) x(k) + B(k) u(k)$$

where $A(k)$ and $B(k)$ are generated by a stationary random process. Is there an equivalent linear time-invariant (LTI) system which will calculate the expected trajectory of $x(k)$?

$$\mathbb E[x(k+1)] = z(k+1) = A_{\text{eq}} z(k) + B_{\text{eq}} u(k)$$

If so, how is it calculated?

Given a discrete-time linear time-varying system (LTV)

$$x(k+1) = A(k) x(k) + B(k) u(k)$$

where $A(k)$ and $B(k)$ are generated by a stationary random process. Is there an equivalent linear time-invariant (LTI) system which will calculate the expected trajectory of $x(k)$?

$$\mathbb E[x(k+1)] = z(k+1) = A_{\text{eq}} z(k) + B_{\text{eq}} u(k)$$

If so, how is it calculated?

If not, are there conditions where this can be calculated?

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edit approved Jan 9, 2017 at 10:08
Rodrigo de Azevedo
edit approved Jan 9, 2017 at 10:08
Rodrigo de Azevedo
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Is there an equivalent line time invariant linear-invariant system for a linear time varying-varying system with specific properties?

Given a discrete time-time linear time varying-varying system: (LTV)

x(k+1) = A(k) * x(k) + B(k) * u(k)$$x(k+1) = A(k) x(k) + B(k) u(k)$$

Where A(k)where $A(k)$ and B(k)$B(k)$ are generated by a stationary random process. Is there an equivalent linear time-invariant (LTI) system which will calculate the expected trajectory of x(k)$x(k)$?

E[x(k+1)] = z(k+1) = Aeq * z(k) + Beq * u(k)$$\mathbb E[x(k+1)] = z(k+1) = A_{\text{eq}} z(k) + B_{\text{eq}} u(k)$$

If so, how is it calculated?

Is there an equivalent time invariant linear system for a linear time varying system with specific properties?

Given a discrete time linear time varying system:

x(k+1) = A(k) * x(k) + B(k) * u(k)

Where A(k) and B(k) are generated by a stationary random process. Is there an equivalent linear time-invariant system which will calculate the expected trajectory of x(k)?

E[x(k+1)] = z(k+1) = Aeq * z(k) + Beq * u(k)

If so, how is it calculated?

Is there an equivalent line time-invariant system for a linear time-varying system with specific properties?

Given a discrete-time linear time-varying system (LTV)

$$x(k+1) = A(k) x(k) + B(k) u(k)$$

where $A(k)$ and $B(k)$ are generated by a stationary random process. Is there an equivalent linear time-invariant (LTI) system which will calculate the expected trajectory of $x(k)$?

$$\mathbb E[x(k+1)] = z(k+1) = A_{\text{eq}} z(k) + B_{\text{eq}} u(k)$$

If so, how is it calculated?

Source Link
Ed Tate
Ed Tate
  • 141
  • 3

Is there an equivalent time invariant linear system for a linear time varying system with specific properties?

Given a discrete time linear time varying system:

x(k+1) = A(k) * x(k) + B(k) * u(k)

Where A(k) and B(k) are generated by a stationary random process. Is there an equivalent linear time-invariant system which will calculate the expected trajectory of x(k)?

E[x(k+1)] = z(k+1) = Aeq * z(k) + Beq * u(k)

If so, how is it calculated?