A system is characterized by the following state equation and output equation (  : input,  : state vector,  : output)

What are the values of  and  for which the poles of the transfer function are at  and  ?

Consider the state-space model

where  are the state, input and output, respectively. The matrices  are given below

The sum of the magnitudes of the poles is __________ (round off to nearest integer).

Consider the state-space description of an LTI system with matrices

For the input, , the value of  for which the steady-state output of the system will be zero, is __________ (Round off to the nearest integer).

Consider a state-variable model of a system

where y is the output, and r is the input. The damping ratio  and the undamped natural frequency  (rad/sec) of the system are given by

Consider a system governed by the following equations

The initial conditions are such that. Let and. Which one of the following is true?

Consider the system described by the following state space representation

 and

If u(t) is a unit step input and , the value of output y(t) at t = 1 sec (rounded off to three decimal places ) is ___________ .

Consider the following state-space representation of a linear time-invariant system.        

 and .

The value of y(t) for  is _______________.

Consider a linear time invariant system , with initial condition at t = 0. Suppose  and  are eigenvectors of  matrix A corresponding to distinct eigenvalues  and  respectively. Then the response x(t) of the system due to initial condition  is        

The following discrete – time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variable x and y. The integration time step is h.         

For this discrete – time system, which one of the following statements is TRUE?

Consider the system described by following state space equations

If u is unit step input, then the steady error of the system is

The state variable formulation of a system is given as

, , and

The response y (t) to a unit step input is

The system  with  is

A system is described by the following state and output equations

Where u(t) is the input and y(t) is the output.

The system transfer function is

A system is described by the following state and output equations

Where u(t) is the input and y(t) is the output.

The state-transition matrix of the above system is

The state space equation of a system is described by

Where x is state vector, u is input, y is output and

The transfer function G(s) of this system will be

The state space equation of a system is described by

Where x is state vector, u is input, y is output and

A unity feedback is provided to the above system G(s) to make it a closed loop system as shown in figure.

For a unit step input r(t), the steady state error In the output will be

A state variable system

, with the initial condition and the unit step input  u(t) has

The state transition matrix

A state variable system

, with the initial condition and the unit step input u(t) has and the state transition equation

The state variable description of a linear autonomous system is X = AX, where X is the two dimensional state vector and A is the system matrix given by         

.  The roots of the characteristic equation are

A second order system starts with an initial condition of without any external input. The state transition matrix for the system is given by.  The state of the system at the end of 1 second is given by

The state transition matrix for the system X = AX & with initial state X(0) is

For the system

with u as unit impulse and with zero initial state, the output, y, becomes

Given the homogeneous state-space equation

The steady state value, given the initial state value of  is

The state-space representation of a system is given by:

Find the Laplace transform of the state transition matrix. Find also the value of  at  if

A system is described by the state equation. The output is given by Y=CX  

Where . Transfer function G(s) of the system is :

The state equation of a linear time-invariant system is given by

(i) Find state transition
(ii) Determine the state vector for t=0 when r(t)=U(t). Assume values of states initially to be zero.

The transfer function for the state variable representation , , is given by