Self-triggered finite-time H∞ control for Markov jump systems with multiple frequency ranges performance

Finite-frequency control for nonlinear semi-Markov jump systems with piecewise transition probabilities

Considering the frequency effect of external disturbances, this paper concerns the finite-frequency control problem for nonlinear semi-Markov jump systems (SMJSs) with piecewise transition probabilities (TPs) via the Takagi-Sugeno (T-S) fuzzy modeling approach. More precisely, the piecewise TPs are assumed to switch stochastically within limits, which implies that the corresponding distributions of sojourn time (ST) also vary randomly. Furthermore, another upper semi-Markov chain is utilized to characterize TPs variation in a finite set. With the aid of Finsler's lemma and Parseval's theorem, sufficient criteria for the controlled SMJS are constructed to meet the desired disturbance attenuation performance in the frequency domain. Then, the mode-dependent controllers are developed to use the TP information more efficiently. In particular, a novel matrix method is proposed to decouple the mode-dependent variables and controller gains by selecting slack matrices. Eventually, a numerical example is transmitted to demonstrate the validity and merits of established results.

Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties

The Markov jump systems (MJSs) are a special case of parametric switching system. However, we know that time delay inevitably exists in many practical systems, and is known as the main source of efficiency reduction, and even instability. In this paper, the stochastic stable control design is discussed for time delay MJSs. In this regard, first, the problem of modeling of MJSs and their stability analysis using Lyapunov-Krasovsky functions is studied. Then, a state-feedback controller (SFC) is designed and its stability is proved on the basis of the Lyapunov theorem and linear matrix inequalities (LMIs), in the presence of polytopic uncertainties and time delays. Finally, by various simulations, the accuracy and efficiency of the proposed methods for robust stabilization of MJSs are demonstrated.