Time-suboptimal feedback design via linear matrix inequalities

In this paper, a time-optimal control problem is considered for plants represented by chains of integrators. A suboptimal solution obtained by using the implicit Lyapunov function approach is proposed in the form of continuous finite-time state feedback regulator. An algorithm for optimal tuning the parameters of the controller is formulated as a finite-dimensional semidefinite program. A robustness-oriented comparison of the optimal and suboptimal solutions in practical implementations of the proposed controller is performed via the numerical example of double integrator.