A robust nonlinear control is designed for stabilizing linear MIMO systems. The presented control law homogenizes a linear system (without its transformation to a canonical form) with a specified degree and stabilizes it in a finite time (or with a fixed-time attraction to any compact set containing the origin) if the degree of homogeneity is negative (positive). The tuning procedure is formalized in LMI form. Performance of the approach is illustrated by numerical and experimental examples.

Robustness with respect to delays is discussed for homogeneous systems with negative degree. It is shown that if homogeneous system with negative degree is globally asymptotically stable at the origin in the delay-free case then the system is globally asymptotically stable with respect to a compact set containing the origin independently of delay. The possibility of applying the result for local analysis of stability for not necessary homogeneous systems is analyzed. The theoretical results are supported by numerical examples.

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A control algorithm for finite-time stabilization of a chain of integrators with arbitrary order is introduced. The method is based on Implicit Lyapunov Function (ILF) approach with applying properties of homogeneous systems. Scheme of control parameter tuning is presented in Linear Matrix Inequality (LMI) form. The method is simple in implementation and does not assume any additional computational on-line procedures that is an improvement with respect to [8], [11]. The theoretical results are supported by numerical simulations.

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