11 Systems with State-multiplicative Noise: Applications

Event‐triggered annular finite‐time H∞$$ {H}_{\infty } $$ filtering for discrete‐time mean‐field stochastic systems

“…For given 𝛾 2 > 0, the FES ( 34) is H ∞ annular finite-time bounded w.r.t. (39), (41) (with M 2 replaced by 𝜃 −T 1 𝛾 2 2 I) and the following inequalities hold…”

“…Notably, due to the existence of mathematical expectations, there are significant differences in certain cases. The mathematical expectations of system state $$$ \mathit{\mathcal{E}x}(t) $$$ and external disturbance $$$ \mathit{\mathcal{E}v}(t) $$$ appear in system dynamics, which means that the mean‐field stochastic $$$ {H}_{\infty } $$$ filtering problem cannot be addressed by the same methods given in References 38 and 39. To tackle this problem, a new Lyapunov functional (LF) is defined, and two equations about $$$ \overline{x}(t)-\mathcal{E}\overline{x}(t) $$$ and $$$ \mathcal{E}\overline{x}(t) $$$ are introduced.…”

H∞‐FIR filtering of disturbed systems using LMI under measurement and initial errors

“…Provided that the H ∞ -FIR filter gain  N is obtained numerically using Theorem 1, the a posteriori H ∞ -FIR filtering estimate is computed by (5) with embedded (6) as…”

“…3 This gives the best practical effect, albeit at expense of the accuracy obtained by optimal tuning. 4 In response to practical needs, different kinds of robust state observers and estimators have been developed during the last decades [5][6][7][8] for adaptive systems, state feedback control, and model predictive control. The most effective robust observers were obtained in the transform domain for linear time-invariant (LTI) systems, by minimizing estimation errors for maximized disturbances using the disturbance-to-error transfer function  .…”

Observer-Based Leader Following Consensus of Nonlinear Multi-agent Systems with a Leader of Bounded Input

“…However, SMC may not provide a satisfied performance for the system with unmatched disturbance [19]. H ∞ techniques offer distinct advantages over classical control methods, particularly in their applicability to problems of involving multivariable systems with crosscoupling between channels [12], [20]- [22]. However, it's important to acknowledge that the use of H ∞ techniques comes with certain challenges.…”