Control Systems, Lecture 12: Stability of Linear Systems / جلسه دوازدهم سیستمهای کنترل

Описание: Lecture 12 — Stability of Linear Systems

In this lecture from the "Control Systems: Classical to Advanced" series, we define stability for linear systems, compare internal (asymptotic) and BIBO viewpoints, and give practical analytical tools you can apply to both continuous- and discrete-time LTI models. You’ll learn how to read stability from state-space eigenvalues and from transfer functions, use Routh–Hurwitz and root-locus intuition, test discrete-time systems in the z-plane, and take the first steps toward designing stabilizing controllers.

What this video covers
• Definitions: Lyapunov stability, asymptotic stability, BIBO stability.
• Stability of LTI systems: relationship between state-space eigenvalues and transfer-function poles.
• Analytical tools: characteristic equation, eigenvalue analysis, Routh–Hurwitz test, root-locus reasoning, Nyquist intuition.
• Transfer-function domain: pole/zero locations and their effect on stability and transient behavior.
• Internal (asymptotic) stability: criteria in state-space and implications for closed-loop design.
• Discrete-time systems: unit-circle test, z-plane interpretation, mapping from s-plane to z-plane.
• Stabilizing control design: basic pole-placement ideas, feedback roles, and practical considerations.

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