Stochastic stability and stabilization for stochastic differential semi‐Markov jump systems with incremental quadratic constraints

Abstract

The problem of the stochastic stability analysis and state feedback stabilization for nonlinear stochastic differential semi‐Markov jump systems with incremental quadratic constraints is investigated in this article. Different from Markovian process, the transition rate is time varying with known bounds and the sojourn time is conformed to the Weibull distribution in semi‐Markov process. Traditional nonlinear constraint such as Lipschitz, one‐sided Lipschitz, and so forth, is extended to incremental quadratic constraint. By the mode‐dependent Lyapunov function and the slack variable method, the sufficient conditions ensuring that the considered systems are stochastically stable are formulated by linear matrix inequalities. Then, a state feedback controller is designed to drive the closed‐loop system stochastically stable. Finally, an example of helicopter is used to illustrate the superiority as well as effectiveness of the results in this treatise.

Consensus control of nonlinear multi‐agent systems with semi‐Markov switching topology and incremental quadratic constraints

“…According to the algorithm in Reference 22, $$$ f\left(\cdotp \right) $$$ satisfies the IQC, and the corresponding incremental multiplier matrix is $$$$ W=\left[\begin{array}{cccc}87.3703& 0& 0& 0\\ {}0& 87.3703& 0& 0\\ {}0& 0& -87.3703& 0\\ {}0& 0& 0& -71.7444\end{array}\right]. $$$$ According to the inequality condition in Theorem 2, the gain matrices $$$ {K}_{\kappa (t)} $$$, $$$ {H}_{\kappa (t)} $$$ and other matrices are available via the LMI toolbox in MATLAB, …”

“…Then, the investigation on IQC systems has draw considerable attention. Under the framework of IQC, the stochastic stability and stabilization problem of semi‐Markov switch systems was presented in Reference 22. Recently, an observer‐based controller for IQC systems subject to disturbances was designed in Reference 23, and a periodic event‐triggered controller for IQC system was proposed in Reference 24.…”

Asynchronous dissipative control for networked time-delay Markov jump systems with event-triggered scheme and packet dropouts

“…Theorem 2. 2 The system (11) is stochastically stable and strictly (µ, ϑ, υ) − γ −dissipative, if there exist matrices Kj ∈ R n u ×n x , V ∈ R n x ×n x , positive matrices Pp ∈ R n x ×n x , Rpj ∈ R n x ×n x , Q ∈ R n x ×n x and a positive diagonal matrix Ḡpj ∈ R n u ×n u , for ∀p, j ∈ S , satisfying where ( Moreover, due to the fact that namely Then, (…”