Quadratic Stability and Stabilization of Uncertain Discrete-Time Linear Systems

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  • 不確かな離散時間線形システムの二次安定性と安定化
  • 不確かな離散時間線形システムの2次安定性と安定化
  • フ タシカナ リサン ジカン センケイ システム ノ 2ジ アンテイセイ ト

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In this paper. we discuss quadratic stability and stabilization of uncertain discrete time linear systems. The uncertainty is supposed to take a polytopic form in the system matrix. It is known that for a polytope of matrices to be quadratically Schur stable, Schur stability of all of it's vertex matrices is necessary and sufficient. Therefore we first show some classes of systems having common quadratic Lyapunov functions. These are derived from the commutativity assumption of a set of matrices. Using this result, we show some classes of the uncertain systems which are quadratically stable.<br>Based on the stability result, it is possible to stabilize the uncertain systems quadratically. We next propose a method of stabilizing the uncertain systems with a state feedback. It is shown that a feedback matrix is obtaind by a linear matrix inequality. Some numerical examples are worked out to illustrate these results.

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