Question: Assume a linear discrete-time system is given by x ( k +1)=[12?21?] x ( k )+[01?] u ( k ) x (0)= x 0?? Where

Assume a linear discrete-time system is given by x(k+1)=[12?21?]x(k)+[01?]u(k)x(0)=x0?? Where x(k) is the state in time step k,u(k) is the control input and x(0) is the initial state. (a) What is the solution of the state x(k) ? (b) Analyze the stability of the system. (c) Analyze the controllability of the system.

Assume a linear discretetime system is given by x(k + 1) = [g i x(k) + ['1']u(k) x(0) = x0 Where x(k) is the state in time step k, u(k) is the control input and 1(0) is the initial state. (a) What is the solution of the state 150:)? (b) Analyze the stability of the system. (c) Analyze the controllability of the system

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

the answer to question (a)(?) 4. The discrete-time state-space representation obtained by sampling a continuous-time system with a zero-order hold at a sampling period 7= 0.1 second is given by x , (...

Q8. Consider a linear discrete-time system S with input x and output y. Suppose S is driven by an input x(k) for 0

Question: Community ecologists draw "food webs" to describe the predator and prey relationships between all organisms living in an area. A theoretical model predicts that a measure of the structure...

Starting from zero initial conditions, i . e . x 0 = 0 , and given some positive integer p , derive a relationship in matrix - vector form between between xp and the input sequence { u 0 , u 1 , u 2...

You are keen on tracking down a 95% certainty span for the mean number of visits for exercise based recuperation patients. The information beneath show the quantity of visits for 14 haphazardly chose...

Hi, Me and my partner need help for all the questions except for the first one. We need step by step explanation. Thank you Note: For questions 241 we assume the discreteetime dynamical system is...

In C only This assignment is designed to provide you some experience writing programs with the C programming language and to get a glimpse of how machine learning works. There is significant hype and...

Decision making The folowing concepts mathematically and give some examples (numerically) which are necessary in probability theory event sample sponce - statistical inference descriptive s....

b) (10 pts) Give an algorithm that solves this problem. You may use/modify/refer to the pseudocode for Knapsack from the lecture notes (below). 4. Consider the following variant of string alignment:...

SOlve appropriately Show that it is undecidable, given the source code of a program Q, to tell whether or not any of the following is true: (i) Q halts on input 0. (ii) Q is total - that is, Q(y)...

Sears, Roebuck and Co. promised to give Forrer permanent employment. Forrer sold his farm at a loss to take the job. Shortly after beginning work, he was discharged by Sears, which claimed that the...

Briefly explain the nature and the purpose of accounting for depreciation (5 marks) The chief accountant of Jitegemea Ltd has encountered difficulties while accounting for fixed assets and the...

1 Where does Federal tax legislation generally originate?

Query Prompt: You work in Operations and are reviewing customer orders. Develop a query so that the output includes the following attributes in this order: the customer last name, the employee last...

Which financial statement is required for a private-purpose trust fund? 1. Statement of revenues, expenses, and changes in net position. 2. Statement of net position. 3. Statement of cash flows. 4....

In the fund financial statements, a government should include a separate column for each of these except 1. Each major enterprise fund. 2. Each major internal service fund. 3. Each major capital...

A pension (and other employee benefit) trust fund would report 1. Expenditures. 2. Expenses. 3. Deductions. 4. Revenue.