Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Quadratic Lyapunov functions for linear systems

Y. V. Venkatesha1

a1 Department of Electrical Engineering, Indian Institute of Science, Bangalore 12, India


The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable system is not identically equal to a unit matrix multiplied by a scalar. The result subsumes that of Lehnigk(1).

(Received April 04 1968)