**6.1.** The stability of the feedback control system of Figure P6.1 is to be determined.

**(a)** Determine the system’s **P** matrix from its state equations.

**(b)** Find the system’s characteristic equation from knowledge of the **P** matrix.

**(c)** Using the Routh–Hurwitz criterion, determine whether this feedback control system is stable.

**6.2.** Stability of the control system of Figure P6.2 is to be determined.

**(a)** Determine the system’s **P** matrix from its state equations.

**(b)** Determine the characteristic equation of this system from knowledge of the **P** matrix.

**(c)** Utilizing the Routh–Hurwitz criterion, determine the necessary relationship between *T*_{1} and *T*_{2} for this system to be stable.

**6.3.** A feedback control system can be represented by a state vector differential equation where

**(a)** Determine the characteristic equation of this control system.

**(b)** Using the Routh–Hurwitz criterion, determine the range of *K* where the system is stable.

**6.4.** Consider the control system of a tracking radar system which operates in two coordinate axes. Its signal-flow graph, which is illustrated in Figure P6.4 indicates that there is electrical coupling between the control systems ...

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