Properties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems

results that include the well-known matrix equality condition [1] as a special case, still allowing arbitrary state weighting matrices. Theorem 6 and Corollary 4 are also new results that weaken the condition on the state weighting matrix. It is known that the terminal weighting matrices presented in this paper can be represented as LMI forms and computed by using existing semi-definite programming methods [21] numerically. The monotonicity of the optimal cost obtained in this paper may be useful for the closed-loop stability of constrained linear systems. A modified quadratic cost problem and feedback stabilization of a linear system, " IEEE Trans. Receding horizon tracking control as a predictive control and its stability properties, " Int. Robust constrained model predictive control using linear matrix inequalities, " Automatica, A quasiinfinite horizon nonlinear model pre-dictive control scheme with guaranteed stability, " Automatica, On the stability of receding-horizon LQ control with zero-state terminal constraint, " IEEE Trans. Automat. , " Stabilizing a discrete, constant, linear system with application to iterative methods for solving the Riccati equation, " IEEE Trans. Au-tomat. On feedback stabilization of time-varying discrete linear systems, " IEEE Trans. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximation, " J. Stabilizing state-feedback design via the moving horizon method, " Int. On stability of constrained receding horizon control with finite terminal weighting matrix, " Auto-Abstract—In this paper, a combined adaptive/variable structure control approach is presented that exploits the good properties of the backstepping procedure and of a second-order sliding-mode control algorithm. This algorithm enables one to attain the conditions = 0, _ = 0 (second-order sliding mode) in a finite time, = 0 being a predefined sliding manifold. The combined approach retains the stability and convergence features of the original adaptive strategy. In addition, it allows one to deal with systems with uncertainties of more general types, ensuring robustness, as well as a reduction in the computational load.