7.1

The differential equations of a plant model are given by

(7.136)

Verify the invertibility and internal stability of the given system (7.136), where (a) a = 1, and (b) a = 3. Find the degenerated system.

7.2

The plant model is given by

(7.137)

Verify the invertibility and internal stability of the given system (7.137), where (a) a = 1, and (b) a = -1. Find the degenerated system.

7.3

The differential equations of a plant model are given by

(7.138)

Verify the invertibility and internal stability of the given system (7.138). Find the degenerated system.

7.4

Verify the invertibility and internal stability of the system

(7.139)

7.5

Verify the invertibility and internal stability of the system

(7.140)

7.6

Verify the invertibility and internal stability of the system

(7.141)

7.7

Verify the invertibility and internal stability of the system

(7.142)

7.8

Verify the invertibility and internal stability of the system

(7.143)

7.9

Verify the invertibility and internal stability of the system

(7.144)

Assume that the inequalities x _i( t) ? 1 ? i, r( t) ? 0.5 hold for all t ? [0, ?). Find the control law of the form (7.91) such that ? _r = 0, , ? ^d ? 10%. Run a computer simulation of the closed-loop system with zero initial conditions. Compare simulation results of the output response with the assignment for r( t)...