(a) Determine the state controllability and observability for the system represented by the following state equation. $$ \begin{gathered} X=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & -2 & -3 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right] u \\ Y=\left[\begin{array}{lll} 3 & 4 & 1 \end{array}\right] x \end{gathered} $$
Explanation
To determine the controllability and observability of the system, we need to find the controllability and observability matrices. The controllability matrix is given by C = [B AB A^2 B]. The observability matrix is given by O = [C; CA; CA^2]. The system is controllable if the controllability matrix has full rank. The system is observable if the observability matrix has full rank.
⬆ Related Topic
📘 Syllabus
View KERALA UNIVERSITY Class 6 Syllabus →
📝 Practice Questions
Practice Previous Year Questions →
🤖 Practice with AI
Generate Practice Question Paper →
📚 Related Concepts
- (a) List down any four key characteristics of Light Rail Transit System (LRT).
- (a) Explain the factors involved in the selection of good alignment for a railway line. Illustrate with necessary sketch
- (a) Explain the functions of rails and various types of rails in use.
- (a) What is negative super elevation? A $1^{\circ}$ curve track diverges from a main curve of $3^{\circ}$ in the opposit
- (a) Why is widening of gauge required on sharp curves? Determine the extent of gauge widening required for a broad gauge