It is shown that for a class of interval matrices we can estimate the location of eigenvalues in a very simple way. This class is characterized by the property that eigenvalues of any real linear combination of member matrices are all real and thus includes symmetric interval matrices as a subclass. Upper and lower bounds for each eigenvalue of such a class of interval matrices are provided. This enables us to obtain Hurwitz stability conditions and Schur ones for the class of interval matrices and positive definiteness conditions for symmetric interval matrices.

A quick evaluation method is proposed to obtain stability robustness measures in polynomial coefficient space based on knowledge of coefficients of a Hurwitz stable nominal polynomial. Two norms are employed: l- and l2-norm, which correspond to the stability hypercube and hyperball in the space, respectively. Just inverting Hurwitz matrix for the nominal polynomial immediately yields closed-form estimates for the size of the hypercube and hyperball.

This letter proposes a pulse width modulated (PWM) control method which can stabilize chaotic orbits onto unstable fixed points and unstable periodic orbits. Some numerical experiments using the Lorenz equation show that chaotic orbits can be stabilized by the PWM control method. Furthermore, we investigate the stability in the neighborhood of an unstable fixed point and discuss the stability condition of the PWM control method.

This letter addresses stability problems of interval matrices stemming from robustness issues in control theory. A quick overview is first made pertaining to methods to obtain stability conditions of interval matrices, putting particular emphasis upon one of them, regularity condition approach. Then, making use of this approach, several new stability criteria, for both Hurwitz and Schur stability, are derived.

An extension is made for a set of systems that have a quadratic Lyapunov function in common for the purpose of analysis and design. The nominal set of system matrices comprises stable symmetric matricies, which admit a hyperspherical Lyapunov function. Based on stability robustness results, sets of matrices are constructed so that they share the same Lyapunov function with the nominal ones.

New equivalent characterizations are derived for Schur stability property of real polynomials. They involve a single scalar parameter, which can be regarded as a freedom incorporated in the given polynomials so long as the stability is concerned. Possible applications of the expressions are suggested to the latest results for stability robustness analysis in parameter space. Further, an extension of the characterizations is made to the matrix case, yielding one-parameter expressions of Schur matrices.

For a real Schur polynomial, estimates are derived for a Schur stability margin in terms of matrix entries or tableau entries in some stability test methods. An average size of the zeros of the polynomial is also estimated. These estimates enable us to obtain more information than stability once a polynomial is tested to be stable via the established Schur stability criterion for real polynomials.

A simple inequality that guarantees stability of perturbed linear state space models is proposed. It is shown that the result is superior to some existing result in sharpness and possesses some advantageous aspects.