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In this section we shall first review technlqes into canonical forms. Then we shall review the invariance property of the Consider conditions for the controllability matrix and observability matrix orming State-Space Equations Into Canonical forms. crete-time state equation and output equation x(k +1) Gx(k) + Hu(k) y(k) Cx(k) + Du(k) We shall review techniques for transforming the state-s (6-30) (6-31) pace equations defined by Equations (6-30) and (6-31) into the following three canonical forms: 1. Controllable canonical form 2. Observable canonical form 3. Diagonal or Jordan canonical form (Note that the diagonal canonical form is a special case of the Jordan canonical form.) It is assumed that the system defined by Equations (6-30) and (6-31) is completely state controllable and completely observable. Controllable Canonical Form. The system defined by Equations (6-30) and (6-31) can be transformed into a controllable canonical form by means of the transformation matrix (6-32 where and (6-i - a-2a 1 an-2 an-3 1 a 1. 0 0

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using the technique pictured, find the controllable canonical form of

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