Sliding mode control design using canonical homogeneous norm

Abstract

Summary The problem of sliding mode control design for a nonlinear plant is studied. The necessary and sufficient conditions of quadratic‐like stability (stabilizability) for a nonlinear homogeneous (control) system are obtained. Sufficient conditions of robust stability/stabilizability are deduced. The results are supported with academic examples of sliding mode control design.

Consistent Discretization of Finite-time Stable Homogeneous Systems

“…It is shown that any generalized homogeneous finite-time stable system admits implicit Euler discretization preserving finite-time convergence. The topological equivalence [29] of homogeneous stable system to a quadratically stable one is utilized for the design of this scheme. Theoretical results are supported with numerical simulations.…”

Generalized Feedback Homogenization and Stabilization of Linear MIMO Systems

“…Definition 5 [9], [5] The dilation d is said to be strictly monotone if ∃β such that d(s) A ≤ e βs for s ≤ 0.…”

“…In particular, local stability of homogeneous system means the global one; if an asymptotically stable system is homogeneous with negative degree, then it is finitetime stable, etc. The present paper deals with generalized homogeneity [12], [5], which is based on groups of linear transformations (linear dilations).…”

Continuous robust fault‐tolerant control and vibration suppression for flexible spacecraft without angular velocity

“…[4][5][6][7] The passive FTC does not require fault detection and diagnostic scheme, and the controllers are designed to be robust against a class of presumed faults. [8][9][10][11][12][13][14] Sliding mode control (SMC) techniques are widely exploited not only in theory but also in practical applications [15][16][17][18][19][20] due to its strong robustness. In the work of Xu et al, 21,22 the FTC approach based on terminal sliding-mode method was presented for finite-time attitude stabilization of satellite, which also resolved the potential singularity problem of traditional terminal SMC designs.…”