Stability Analysis of Discrete-Time Switched Linear Systems With Parametric Uncertainties

This paper considers the stability problem of discrete-time switched linear systems in the presence of parametric uncertainties. this type of uncertainty is sometimes called structured uncertainty because of its known structure. however, some of the parameters in the system are uncertain. from a practical viewpoint, it is important to guarantee the robust stability of uncertain switched systems. therefore, based on the structure of the uncertainty matrix and the common lyapunov function for the nominal switched system, sufficient conditions for robust exponential stability of the discrete-time uncertain switched system (under any switching signal) are derived. these sufficient conditions are formulated in terms of matrix inequalities and using fixed values for some parameters, they will be solved via lmi techniques and based on numerical methods. moreover, a procedure is proposed to determine the maximum admissible bounds of the uncertain parameters to guarantee the exponential stability of the uncertain switched system. finally, numerical examples are provided to verify the proposed theoretical results.