Proportional integral observer based tracking control design for Markov jump systems

Abstract

With the use of proportional integral observer, this article intends to discuss an effective output tracking control and disturbance rejection problem for an input time-delayed Markov jump system with state dependent nonlinearities and randomly occurring uncertainties. Notably, the proportional integral observer incorporates both proportional and integral loop, where the presence of additional loop provides unbiased state estimation. Moreover, an improved equivalent input disturbance approach with a gain factor is considered to enhance better disturbance estimation and rejection performance. Naturally, Smith predictor is commenced to handle input time delays. Subsequently, the combination of improved equivalent input disturbance with Smith predictor guarantees the desired tracking performance with input time delays and external disturbances. By endowing Lyapunov stability theory, a set of sufficient conditions is developed in the frame of linear matrix inequalities to promise the asymptotically stability of the closed-loop system. Subsequently, the explicit form of the desired proportional integral gain matrices are parameterized using the matrix inequality techniques. The superiority of our proffered control technique are validated through two numerical examples, which includes a practical model namely RLC circuit.