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In this paper, we investigate the problems of robust stability andℋ  ∞    -estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteedℋ  ∞    -performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.

mathematical problems in engineering

Robust stability and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\mathcal{H}_\infty$" id="E1"><mml:msub><mml:mi>ℋ</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math>-estimation for uncertain discrete systems with state-delay

Robust stability and ℋ∞-estimation for uncertain discrete systems with state-delay