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This work is concerned with the passive realizability problem for a biquadratic impedance with double poles and zeros as a seven-element series–parallel $RLC$ (damper-spring-inerter) network, which is a series or a parallel connection of two networks: a three-element series–parallel network and a four-element series–parallel network. First, a necessary and sufficient condition is obtained for the realizability of a biquadratic impedance with double poles and zeros as a series–parallel network containing no more than six elements (see Theorem ). Then, the main theorem is presented (see Theorem ), which is derived for three-reactive-element, four-reactive-element, and five-reactive-element settings, respectively (see Lemmas –). The results can be directly utilized to physically construct a passive mechanism containing dampers, springs, and inerters, which can be regarded as a passive controller for some mechanical control systems. [ABSTRACT FROM AUTHOR]

In this note, a discrete-time modified algebraic Riccati equation (MARE) is investigated. First, the analytic solutions of the homogeneous MARE for controllable single-input systems are explicitly obtained in terms of the system eigenvalues. For anti-Schur systems, the stabilizing, and positive definite solution is proposed. Furthermore, the maximal solution and the solution bound are analyzed for the nonhomogeneous MARE. [ABSTRACT FROM AUTHOR]

This paper studies the passive network synthesis problem of biquadratic impedances as five-element bridge networks. By investigating the realizability conditions of the configurations that can cover all the possible cases, a necessary and sufficient condition is obtained for biquadratic impedances to be realizable as two-reactive five-element bridge networks. Based on the types of the two reactive elements, the discussion is divided into two parts, and a canonical form for biquadratic impedances is utilized to simplify and combine the conditions. Moreover, the realizability result for the biquadratic impedance is extended to the general five-element bridge networks. Some numerical examples are presented for illustration. [ABSTRACT FROM AUTHOR]

This paper addresses the challenging problem of designing an adaptive feedback strategy for simultaneous identification and stabilization for a class of nonlinearly parameterized uncertain systems in discrete time. The Nonlinear Least Squares (NLS) algorithm is applied to estimate the unknown parameters, and it turns out to be the standard Least Squares (LS) algorithm whenever the model is linearly parameterized. Based on this algorithm, both the strong consistency of the estimator and the global stability of the system are achieved with the output feedback design for the scalar-parameter case. [ABSTRACT FROM PUBLISHER]

Most existing works on adaptive control of discrete-time systems focus on the case of linear parametrization. For nonlinearly parameterized systems, the stabilizability turns out to be an intractable issue. This technical note is devoted to seeking the essential factors that determine the stabilizability of nonlinearly parameterized discrete-time systems. A sufficient condition imposed on the structures of the system functions is established. Analysis shows that the sensitivity function of unknown parameters plays a crucial role in characterizing the uncertainties of parameterized systems. One of the implications of this result is that arbitrarily growing nonlinearities in the uncertain model may be allowed for global stabilization. [ABSTRACT FROM AUTHOR]

This paper investigates the simplified realization problem of a special class of positive-real admittances similar to biquadratic functions but with an extra pole at the origin, which is widely used in the analysis of suspension systems. The results in this paper are motivated by passive mechanical control with the inerter. The concept of strictly lower complexity is first defined, whose indices in this paper are the total number of elements, the number of resistors (dampers), and the number of capacitors (inerters). We then derive a necessary and sufficient condition for this class of admittance to be realized by the networks that are of strictly lower complexity than the canonical realization by the Foster Preamble method. To solve this problem, it is shown that it suffices to consider the following: 1) networks with at most four elements, 2) irreducible five-element resistor-inductor (RL) networks, and 3) irreducible five-element resisitor-inductor-capacitor (RLC) networks. Other cases are shown to be impossible. By finding their corresponding network configurations through a series of constraints and deriving the corresponding realizability conditions, the final condition can be obtained. Finally, the U-V plane and numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper is concerned with a class of random jump systems represented by transition operators, which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case. A series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios. The stability criteria obtained are further extended to Markov jump linear systems with infinite states, and hence a unified approach to describing the almost sure stability of MJLSs is addressed under this context. All the results in the work are developed for both the continuous- and discrete-time systems. [ABSTRACT FROM AUTHOR]

In this technical note, we will investigate the maximum capability and limitations of the feedback mechanism in globally stabilizing a basic class of discrete-time nonlinearly parameterized dynamical systems with multiple unknown parameters. Both “possibility” and “impossibility” theorems together with a fairly complete characterization on the capability of feedback will be presented. It will be seen that to characterize the feedback capability, the growth rates of the sensitivity functions of the nonlinear dynamics with respect to the uncertain parameters play a crucial role, and a suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary. [ABSTRACT FROM AUTHOR]

State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized. [ABSTRACT FROM AUTHOR]