On properties of state variable stabilizing feedback of a special kind for linear time-invariant regulators

Some interesting properties of a limiting case of linear optimal regulators with quadratic performance index and prescribed degree of stability are discussed. A series of LSVF control laws may be generated by varying a scalar parameter α which specifies the minimum modulus of the real part of the closed-loop poles. All such control laws guarantee a minimum amount of phase and gain margins but differ in speed of error recovery. Explicit algebraic relations for computing feedback laws and Nyquist plots are provided for single input -order systems.