Internal and External Stabilization of Linear Systems with Constraints by Ali Saberi Anton A. Stoorvogel & Peddapullaiah Sannuti

Author:Ali Saberi, Anton A. Stoorvogel & Peddapullaiah Sannuti
Language: eng
Format: epub
Publisher: Birkhäuser Boston, Boston, MA

Step 1 (Controller design for the zero dynamics)

We now focus our design for the first subsystem (8.2) while viewing z as an input variable. At first, we let and rewrite subsystem (8.2) as

(8.5)

We note that the conditions of the theorem imply that all the eigenvalues of A 11 are in the closed left-half plane. As will become transparent in the design for our second subsystem, we need to choose a δ2 such that

(8.6)

where

(8.7)

Clearly, such a δ2 exists since is bounded.

Our objective is to design a stabilizing feedback z 0 = f(x 1) such that the equilibrium point of the closed-loop system of (8.5) and z 0 = f(x 1) with v = 0 is asymptotically stable. Moreover, for all v satisfying the bound

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