Abstract
In this paper, H ∞ control for the uncertain switched nonlinear cascade systems with passive and nonpassive subsystems is investigated. Based on the average dwell time method, for any given passivity rate, average dwell time, and disturbance attenuation level, the feedback controllers of the subsystems by predetermined constants are designed to solve the exponential stability and L 2 -gain problems of H ∞ control for switched nonlinear cascade systems. Two examples are provided to demonstrate the effectiveness of the proposed design method.
Highlights
With the development of scientific computing technology, the research on H∞ control problems of nonlinear systems has been greatly promoted, and the results of nonlinear control problems continue to emerge [1, 2]
Stability was inferred from the passivity described by using multiple storage functions [10]. e necessary and sufficient conditions were obtained for the local passivity of discrete-time switched nonlinear systems which consisted of passive and nonpassive modes, and the passivity of the affine system was studied [9]
Based on the method of average dwell time, we give sufficient conditions to ensure the solvability of the problem avoiding the Lyapunov function construction by the storage functions and reducing the computational complexity of the solution
Summary
With the development of scientific computing technology, the research on H∞ control problems of nonlinear systems has been greatly promoted, and the results of nonlinear control problems continue to emerge [1, 2] These methods usually bring a difficulty that needs to solve the Hamilton–Jacobi equation. E stability of two types of passive H∞ control for discrete-time linear switched systems was considered by multiple storage functions [12, 13]. In this paper, based on the method of average dwell time, the robust H∞ control problem for a class of passive uncertain cascade switched systems with passiveness is considered. For passive subsystems and nonpassive subsystems, we design controllers and apply the multiple storage functions method to solve the stability and L2-gain of the nonlinear uncertain cascade switched system under the given conditions. Notions: Rn is the n-dimensional real Euclidean space; T denotes the matrix transposition; λminQ1, Q2 means the smallest eigenvalue of the matrices Q1 and Q2, and λmaxQ1, Q2 is the largest; ‖ · ‖ is the Euclidean norm of vector; LfV(x) stands for LfV(x) (zV(x)/zxT)f(x), where f(x), V(x) ∈ C1[Rn, R]; means ∞ 0 |g(t)|2dt < ∞
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