Passive parametric macromodeling by using Sylvester state-space realizations

A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. The direct parameterization of poles and residues may be not appropriate, due to their possible non-smooth behavior with respect to design parameters. This is avoided in the proposed technique, by converting the pole-residue description to a Sylvester description which is computed for each root macromodel. This technique is used in combination with suitable parameterizing schemes for interpolating a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels. The key features of the present approach are first the choice of a proper pivot matrix and second, finding a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester technique for parametric macromodeling

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Weakly coprime factorization and state-feedback stabilization of discrete-time systems

Abstract: The LQ-optimal state feedback of a finite-dimensional linear time-invariant sys-tem determines a coprime factorization NM−1 of the transfer function. We show that the same is true also for infinite-dimensional systems over arbitrary Hilbert spaces, in the sense that the factorization is weakly coprime, i.e., Nf,Mf ∈ H2 = ⇒ f ∈ H2 for every function f. The factorization need not be Bézout coprime. We prove that every proper quotient of two bounded holomorphic operator-valued func-tions can be presented as the quotient of two bounded holomorphic weakly coprime func-tions. This result was already known for matrix-valued functions with the classical definition gcd(N,M) = I, which we prove equivalent to our definition. We give necessary and sufficient conditions and further results for weak coprimeness and for Bézout coprimeness. We then establish a variant of the inner-outer factorization with the inner factor being “weakly left-invertible”. Most of our results hold also for continuous-time systems and many are new also in the scalar-valued case