The document discusses state space representations and solutions of discrete-time state space equations. It describes how the state at any time k can be obtained directly by recursion using the state space equations. It also introduces the concept of the state transition matrix, which allows writing the solution as a matrix exponential involving the state transition matrix. Finally, it discusses using the z-transform approach to solve discrete-time state equations.

1. c
CAREER POINT UNIVE
MAJOR ASSIGNMENT
- Design & Discreatization of continuous time
state space equations

2. STATE SPACE REPRESENTATIONS OF DISCRETE-TIME SYS
Nonuniqueness of State Space Representations

3. STATE SPACE REPRESENTATIONS OF DISCRETE-TIME SYS
Nonuniqueness of State Space Representations
≡

4. SOLVING DISCRETE TIE STATE-SPACE EQUATIONS
Solution of LTI Discrete-Tim State Equations
x(k) or any positive integer k may be obtined directly by recursion, as follows:

5. SOLVING DISCRETE TIE STATE-SPACE EQUATIONS
State Transition Matrix
It is possible to write the solution of the homogeneous state equation
as
state transition matrix(fundamental matrix) :

6. SOLVING DISCRETE TIE STATE-SPACE EQUATIONS
State Transition Matrix

7. SOLVING DISCRETE TIE STATE-SPACE EQUATIONS
z Transform Approach to the Solution of Discrete-Time State Equations

8. SOLVING DISCRETE TIE STATE-SPACE EQUATIONS
z Transform Approach to the Solution of Discrete-Time State Equations
Example:
a)
b)

9. Coding
• P1=[8 56 96];
• Q1=[1 4 9 10];
• Sys=tf(P1,Q1)
• Roots(P1);
• Roots(Q1);
• pzMAP(sys);

10. Figure

11. Coding.2
• Num=[49];
• Den=[ 1 4 9 ];
• Sys=tf(num,den);
• load ltiexamples
• ltiview

12. Graph

13. Coding
• Num=[49 89 96];
• Den=[1 4 9];
• Sys=tf[Num,Den];
• Load ltiexamples
• ltiview

14. Graph