From 7feebfcb9a9807eaa7b0bb2c0a790702973959db Mon Sep 17 00:00:00 2001
From: ysfemregultekin <74116999+ysfemregultekin@users.noreply.github.com>
Date: Thu, 16 Jan 2025 02:59:08 +0300
Subject: [PATCH] Update EE402_Lecture_12.tex

In the definition of MIMO stability there is typo
at 12-3 there is typo: x[k] is not written in y[k] equation
at 12-7 there is typo: x[k] is not written in y[k] equation
---
 METU-EE402/Lecture 12/EE402_Lecture_12.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/METU-EE402/Lecture 12/EE402_Lecture_12.tex b/METU-EE402/Lecture 12/EE402_Lecture_12.tex
index 91c343d..6716973 100644
--- a/METU-EE402/Lecture 12/EE402_Lecture_12.tex	
+++ b/METU-EE402/Lecture 12/EE402_Lecture_12.tex	
@@ -114,7 +114,7 @@ \section*{State-Space Representation of DT Systems}
 %
 \begin{itemize}
   \item $m = r = 1$, the system represents a SISO system 
-  \item $m > 1 \ , \  r < 1$, the system represents a MIMO system 
+  \item $m > 1 \ , \  r > 1$, the system represents a MIMO system 
   \item $m = 1 \ , \ r > 1$, the system represents a MISO system 
   \item $m > 1  \ , \ r = 1$, the system represents a SIMO system 
 \end{itemize}
@@ -198,7 +198,7 @@ \subsubsection*{Reachable/Controllable Canonical Form}
     \\ 1 \end{array} \right] u[k]
 \\
 y[k] &= \left[ \begin{array}{ccc} (b_3 - b_0 a_3) &  (b_2 - b_0 a_2) &
-                                                                       (b_1 - b_0 a_1) \end{array} \right]
+                                                                       (b_1 - b_0 a_1) \end{array} \right] x[k]
 + b_0 u[k]
 \end{align*}
 %
@@ -289,7 +289,7 @@ \subsubsection*{Observable Canonical Form}
   \left[ \begin{array}{c} b_3 - b_0 a_3 \\ b_2 - b_0 a_2
     \\ b_1 - b_0 a_1 \end{array} \right] u[k]
 \\
-y[k] &= \left[ \begin{array}{ccc} 0 & 0 & 1 \end{array} \right]
+y[k] &= \left[ \begin{array}{ccc} 0 & 0 & 1 \end{array} \right] x[k]
 + b_0 u[k]
 \end{align*}
 %