Mihaly Petreczky

Realization theory for linear switched systems : Formal power series approach

The paper deals with the realization theory of bilinear switched systems. Necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a bilinear switched system. Characterization of minimal realizations is presented. The paper treats two types of bilinear switched systems. The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences is admissible, but within this restricted set the switching times are arbitrary. The paper uses the theory of formal power series to derive the results on realization theory. Partial realization theory is also discussed in the paper.

Realization Theory for Linear Hybrid Systems

The paper develops realization theory for linear hybrid systems, i.e., hybrid systems in continuous-time without guards whose continuous dynamics is determined by linear control systems and whose discrete dynamics is determined by a finite-state automaton. We will formulate necessary and sufficient conditions for the existence of a realization. We will show that minimality is equivalent to observability and span-reachability, and that minimal systems are isomorphic. In turn, observability and span-reachability can be characterized by rank conditions.

Application of Supervisory Control Synthesis to a Patient Support Table of a Magnetic Resonance Imaging Scanner

In this paper, we present a case-study on application of Ramadge-Wonham supervisory control theory (abbreviated by SCT in the sequel) to a patient support system of a magnetic resonance imaging (MRI) scanner. We discuss the whole developmental cycle, starting from the mathematical models of the uncontrolled system and of the control requirements, and ending with the implementation of the obtained controller on the actual hardware. The obtained controller was tested on the physical system. In this case study, we attempted to build the models in a modular way, in order to decrease the computational complexity of the controller synthesis and to improve the adaptability of the models. An important advantage of SCT is that it allows automatic generation of the controller, and that it can thus improve adaptability of the control software. We also briefly discuss our experience on the adaptability of the control software, obtained in the course of this case study.

Reachability of Linear Switched Systems: Differential geometric approach

The paper investigates the structure of the reachable set of linear switched systems. The structure of the reachable set is determined using techniques from classical nonlinear systems theory, namely, the theory of orbits developed by H. Sussman and the realization theory for nonlinear systems developed by B. Jakubczyk.

Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control

In this paper we investigate the stability analysis of nonlinear sampled-data systems, which are affine in the input. We assume that a stabilizing controller is designed using the emulation technique. We intend to provide sufficient stability conditions for the resulting sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling intervals, for which stability is ensured. The main idea of the paper is to address the stability problem in a new framework inspired by the dissipativity theory. Furthermore, the result is shown to be constructive. Numerically tractable criteria are derived using linear matrix inequality for polytopic systems and using sum of squares technique for the class of polynomial systems.

On the notion of persistence of excitation for linear switched systems

The paper formulates the concept of persistence of excitation for discrete-time linear switched systems. In addition, the paper provides sufficient conditions for an input signal to be persistently exciting. Persistence of excitation is formulated as a property of the input signal, and it is not tied to any specific identification algorithm. The results of the paper rely on realization theory and on the notion of Markov-parameters for linear switched systems.

Realization theory of stochastic jump-Markov linear systems

We present a stochastic realization theory for stochastic jump-Markov linear systems (JMLSs). We derive necessary and sufficient conditions for existence of a realization, along with a characterization of minimality in terms of reachability and observability. We also sketch a realization algorithm and argue that minimality can be checked algorithmically. The main tool for solving the stochastic realization problem for JMLSs is the formulation and solution of a stochastic realization problem for a general class of bilinear systems with nonwhite-noise inputs using the theory of formal power series.

Model Reduction by Nice Selections for Linear Switched Systems

A moment-matching method for model reduction of linear switched systems (LSSs) is presented. The method can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant (LTI) systems. The procedure is based on the so called “nice selections,” which represent a choice of basis in the reachability or observability space of the LSS. The framework can also be used for exact matching of the input-output behavior of an LSS with a reduced order LSS for a specific switching sequence. Conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples.

Model reduction by moment matching for linear switched systems

A moment-matching method for the model reduction of linear switched systems (LSSs) is developed. The method is based upon a partial realization theory of LSSs and it is similar to the Krylov subspace methods used for moment matching for linear systems. The results are illustrated by a numerical example.

Affine LPV systems: Realization theory, input-output equations and relationship with linear switched systems

We formulate a Kalman-style realization theory for discrete-time affine LPV systems. We characterize those input-output behaviors which exactly correspond to affine LPV systems. In addition, we present necessary and sufficient conditions for minimality of affine LPV systems and show that equivalent minimal realizations are unique up to isomorphism. The results are derived by reducing the problem to the realization problem for linear switched systems. In addition, we show that an input-output map has a realization by an affine LPV system if and only if it satisfies certain types of input-output equations.