H_∞ Observer-Based Control Design for Switched Positive Systems Including Interval Uncertainties, Unstable Modes and Time-Varying Delay

The purpose of this study is to present a practical approach in which the effect of performance degradation and instability factors such as exogenous disturbances, parametric uncertainties, time-varying delay, and unstable modes can reduce to the minimum possible amount in linear switched positive systems. To reduce the effect of the mentioned destructive factors and to strengthen the robust design of switched positive systems, in this paper, instead of using the co-positive Lyapunov function along with the L1-gain, the quadratic Lyapunov-Krasovskii function utilized along with the L2-gain, which leads to the design of H_∞ performance. The latter method, especially when there is a requirement to estimate the parameters with the support of the output feedback approach by minimizing the interface parameters, provides the feasibility of designing a more convenient and efficient observer-based controller. The necessary and sufficient conditions for solving the problem concerning the positivity of the system, disturbance attenuation, and parametric uncertainties are expressed by two theories and implemented by the linear matrix inequality technique. The results of this technique's solution include the gains of the controller and observer. Considering that stable and unstable modes are in this system, it is necessary to guarantee the exponential stability of the whole system by the controllers and designing the average dwell-time switching regime. Finally, illustrative examples, including numerical, practical, and comparative, are presented to show the efficiency and performance of different aspects of the proposed approach. The smallness of the mean square error values in the example compared with the output feedback method in linear programming confirms the capabilities of the presented approach. For instance, the mean square error of the system output for the method of this paper is 0.008 and for the compared approach is 0.081.