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The finite-time H∞ control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-time H∞ for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfies L2 gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method

mathematical problems in engineering

Robust Finite-Time<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Control for Linear Time-Varying Descriptor Systems with Jumps

Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps