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.