State Space Analysis
The state of a dynamic system is the smallest set of variable (Called state variable) such that the knowledge of such variable at t=t0 together with the knowledge of input for t> =t0 completely determines the behaviour of the system for any time t=t0 .
State variables
A state variable is one of the sets of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behavior in the absence of any external forces affecting the system. Models that consist of coupled first-order differential equations are said to be in state-variable .
State Vector
Two approaches are available for the analysis and design of feedback control systems. The first is known as the classical, or frequency-domain, technique. This approach is based on converting a system’s differential equation to a transfer function, thus generating a mathematical model of the system that algebraically relates a representation of the output to a representation of the input. Replacing a differential equation with an algebraic equation not only simplifies the representation of individual subsystems but also simplifies modeling interconnected subsystems.
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