Linear Systems

6.3    Non-Fragile H_∞ Controller Design for Continuous-Time Systems

In this section, the non-fragile dynamic output feedback H_∞ controller design for continuous-time systems with the interval type of gain variations is considered.

6.3.1    Problem Statement

Consider a continuous-time linear time-invariant model described by

$\begin{array}{lll}\dot{x}\left(t\right)\hfill & =\hfill & Ax\left(t\right)+B_1\omega \left(t\right)+B_{2}u\left(t\right),\hfill \\ z\left(t\right)\hfill & =\hfill & C_{1}x\left(t\right)+D_{12}u\left(t\right),\hfill \\ y\left(t\right)\hfill & =\hfill & C_{2}x\left(t\right)+D_{12}\omega \left(t\right),\hfill \end{array}$

(6.38)

where x(t) ∈ Rⁿ is the state, u(t) ∈ R^m is the control input, y(t) ∈ R^p is the measured output, ω(t) ∈ R^r is the disturbance input, z(t) ∈ R^q is the regulated output, and A, B₁, B₂, C₁, C₂, D₁₂, and D₂₁ are known constant matrices of appropriate dimensions.

And for system (6.38), consider a dynamic output feedback controller with gain variations ...