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Modern Control Theory By U.A Bakshi

**Modern Control Theory By U.A Bakshi**

## Modern control theory

In contrast to the frequency domain analysis of the **classical control theory**, modern control theory utilizes the **time-domain state space representation, **a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations.

To abstract from the number of inputs, outputs and states, the variables are **expressed as vectors and the differential and algebraic equations are written in matrix** form (the latter only being possible when the dynamical system is linear).

**The state space representation** (also known as the **"time-domain approach"**) provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down **Laplace transforms** to encode all the information about a system. Unlike the **frequency domain approach**, the use of the state space representation is not limited to systems with linear components and zero initial conditions. **"State space"** refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.

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