## Analysis and design of discrete linear control systems |

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algebraic Riccati equation Ax(z calculate causal rational functions causal rational matrices characteristic polynomial closed-loop system column degrees condition covariance covariance matrix deadbeat compensator deadbeat gain deadbeat observer decoupling defined denote diag diophantine equations divisor dual dynamic compensation dynamics assignment eigenvalues equivalent Example exists finite causal rational follows greatest common divisor Hence implies infinite zero input integer invariant polynomials Kalman Kucera L-chain left invertible Lemma linear system LQ predictor LQ regulator minimal model matching non-singular non-singular matrix obtained orthogonal pair F prime polynomial matrices Proof quadratic random sequence rational matrix reachability indices reconstruction relatively left prime relatively prime relatively right prime result Riccati equation row degrees row reduced satisfy similarity invariants solution pair spectral factorization stability matrix stabilizable stable causal rational static state feedback Step strictly causal structure algorithm system F Tc(z Theorem transfer function Ts(z unique z]-unimodular