Robust H _∞ control for uncertain Markovian jump systems with mixed delays

Abstract

We scrutinize the problem of robust H ∞ control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H ∞ control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions for delay-dependent robust H ∞ control criteria are obtained in terms of linear matrix inequalities (LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

H∞ control for networked semi‐Markovian jump systems with generally incomplete transition probabilities and distributed delays

“…On the other hand, the research efforts given to S-MJNCSs were still limited, especially for switching systems with time-delay, [26][27][28] which may cause poor performance, oscillation, and even instability. 7 To deal with delay problem, 29,30 proposed some methods to analyze the effect of the network transmission delay on linear NCSs.…”

Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

“…Moreover, it has been well recognised that, delays and uncertainties are frequently encountered in many practical systems and often a primary source of instability and performance degradation of a control system [15]. Therefore, it is important to incorporate uncertainties and delays in the model of various systems [14, 16–21]. In addition, as we all know, system properties usually can be formalised as frequency domain inequality (FDI) conditions on the transfer function, such as the bounded‐realness and the positive‐realness [22].…”