Abstract
Robust stabilization and H ∞ controller design for uncertain systems with impulsive and stochastic effects have been deeply discussed. Some sufficient conditions for the considered system to be robustly stable are derived in terms of linear matrix inequalities (LMIs). In addition, an example with simulations is given to better demonstrate the usefulness of the proposed H ∞ controller design method.
Highlights
Analysis and synthesis of dynamical systems with impulsive effects have attracted recurring interest for the past few decades [1,2,3]
Parameter uncertainties appear in stochastic impulsive systems, and exponential stability was analyzed in [22], guaranteed cost control was discussed in [23]
The studies of robust stabilization and H∞ controller design are conducted for an uncertain stochastic system with impulsive effects
Summary
Analysis and synthesis of dynamical systems with impulsive effects have attracted recurring interest for the past few decades [1,2,3]. The theory and application of stochastic differential equations have made great progress because it has played a key role in many fields; for example, option investment, population growth forecast, system control and filtering [17,18,19,20,21]. The studies of robust stabilization and H∞ controller design are conducted for an uncertain stochastic system with impulsive effects. The note has the following arrangement: Section 2 begins with the problem formulation and reviews some useful definitions and lemmas; Section 3 discusses the robust stability and robust stabilization; Section 4 develops LMI-based H∞ controller design method; Section 5 gives an example, which illustrates the applicability of the theoretical results; Section 6 summarizes the full text. K · kL2 (respectively, k · kl2 ) represents the L2 [0, ∞) (respectively, l2 [0, ∞)) norm on [0, ∞); while k · kE2 indicates the norm in L2 ((Ω, F, P), [0, ∞)); (Ω, F, P)) is the complete probability space with Ω the sample space and F the σ-algebra of subsets of the sample space; E (·) corresponds to the mathematical expectation; the maximum (minimum) eigenvalues of a matrix are represented by λmax (·) (λmin (·))
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