Related papers: State space realization of even generalized positi…
We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. We then exploit this result…
There are four variants of passive, linear time-invariant systems, described by rational functions: Continuous or Discrete time, Positive or Bounded real. By introducing a quadratic matrix inequality formulation, we present a unifying…
The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently…
For discrete-time causal linear input/state/output systems, the Bounded Real Lemma explains (under suitable hypotheses) the contractivity of the values of the transfer function over the unit disk for such a system in terms of the existence…
Hyper-Positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this…
We provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers. We exhibit a non-trivial real linear system which is not controllable by real static…
Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
This is the third installment in a series of papers concerning the Bounded Real Lemma for infinite-dimensional discrete-time linear input/state/output systems. In this setting, under appropriate conditions, the lemma characterizes when the…
Positive real odd matrix functions, often referred to as positive real lossless matrix functions, play an important role in many applications in multi-port electrical systems. In this paper we present closer analogues to some of the known…
For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly…
We here characterize the minimality of realization of arbitrary linear time-invariant dynamical systems through (i) intersection of the spectra of the realization matrix and of the corresponding state submatrix and (ii) moving the poles by…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
Finding a positive state-space realization with the minimum dimension for a given transfer function is an open problem in control theory. In this paper, we focus on positive realizations in Markov form and propose a linear programming…
This article deals with the implementation of the Smith Predictor for state feedback control in state space representation. The desired control law, obtained using partial differential equations and backstepping control, contains an…
In this report we deal with the problem of global output feedback stabilization of a class of $n$-dimensional nonlinear positive systems possessing a one-dimensional unknown, though measured, part. We first propose our main result, an…
We investigate state feedback and observation for infinite-dimensional linear systems, including a variety of partial differential equations with boundary control and observation. We extend the modulating function approach to…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
For a broad class of nonlinear systems, we construct smooth control-Lyapunov functions whose derivatives along the trajectories of the systems can be made negative definite by smooth control laws that are arbitrarily small in norm. We…
A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage…