Continuous-time non-minimal state-space design

A continuous time non-minimal state-space (NMSS) representation is shown to be explicitly related to the underlying minimal state-space observer/state feedback design method and, moreover, the corresponding state feedback gains are explicitly related. This result provides a starting point for NMSS methods in the continuous-time domain. Numerical examples are given which illustrate the underlying relationship.     

增广非最小状态空间法的稳定平台预测控制研究

针对传统的模型预测控制器鲁棒性较差及模糊PID控制系统比较复杂的问题,提出了利用增广非最小状态空间模型与模型预测控制相结合的稳定平台预测控制。建立了稳定平台广义被控对象的数学模型,以增广形式的非最小状态空间模型为基础,结合滚动时域控制原则和线性二次型最优控制,通过对稳定平台离散模型的非最小状态空间形式进行增广变换,给出了基于Laguerre函数的状态反馈增益矩阵算法,设计了增广非最小状态模型下的预测控制器,实现了对导向钻井稳定平台控制系统的仿真研究。仿真结果表明稳定平台预测控制系统可以很好地满足钻井工程对控制精度和动态特性的要求,而且对有时变性的盘阀摩擦干扰力矩及模型参数摄动具有较强的鲁棒性。     

A stable state-space realization in the formulation of H∞norm computation

In the two block H^inftyoptimization problem, usually we are given the state-space realizations of the proper rational matricesR_{1}(s)andR_{2}(s)whose poles are all the open right-half plane. Two problems are studied in the note. The first is the evaluation ofphi(s)R_{1}(s)ats = s_{k}, k = 1, 2, ..., n, wherephi(s)is an inner function whose zeros{s_{k}, k = 1, 2, ..., n }are the poles ofR_{1}(s). This evaluation is essential if Chang and Pearson's method is used for computing the optimal H^inftynorm. The problem is solved in state space via the solutions of Lyapunov equations. Neither polynomial matrix manipulations nor numerical pole-zero cancellations are involved in the evaluation. The second problem is to find a stable state-space realization ofS(s) = U(s)R_{2}(s)whereU(s)is an inner matrix. This problem arises in the spectral factorization ofgamma^{2} - R_{2}^{ast}R_{2}. Doyle and Chu had a method for constructing stableS(s)based on a minimal realization ofR_{2}(s). An alternate method is proposed. The alternate method does not require a minimal realization ofR_{2}(s)and only a Lyapunov equation is involved.     

Residual models and stochastic realization in state-space identification

This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.     

平衡功率放大器的设计与实现

设计了一个工作频段为902MHz～928MHz、输出功率为32dBm、应用于读卡器系统的末级功率放大器。为了在工作频段内实现平坦的功率增益并获得良好的输入、输出驻波比,本功率放大器采用平衡放大技术设计。仿真优化和实际测试表明,在整个工作频段内放大器的增益平坦度小于±0.5dB,输入、输出驻波比小于1.5,完全满足设计指标要求。     

Minimal stable partial realization

In this paper two equivalent sets of necessary and sufficient conditions for the existence of an asymptotically stable partial realization are developed. Both sets are expressed as multivariable polynomial equations which may be tested for the existence of a solution in a finite number of rational steps via decision methods. Should a solution exist, it may be evaluated with the aid of polynomial factorization. The first set of conditions are based on results due to Ho and Kalman, and are useful for the case where the number of specified Markov parameters is greater than the order of the realization. For other cases, the second set of conditions which include results from a companion paper on minimal observers, require less computational effort to be tested.     

Three-dimensional discrete-time lossless bounded real functions: minimal state-space realization

A simple technique for state-space realization of 3-dimensional discrete-time lossless bounded real functions is presented. The state-space matrices are of minimal dimension and are derived from the corresponding circuit implementation. The efficiency of the technique is due to the fact that in order to determine the 3D state-space model the circuit implementation is no longer needed because the solution is given in closed form.     

Toward time-varying balanced realization via Riccati equations

This paper presents a new approach for solving balanced realization problems with emphasis on the time-varying case. Instead of calculating the exact solutions for balancing at each time instant, we estimate with arbitrary accuracy the balancing solutions by means of Riccati equations associated with the balancing problems Under uniform boundedness conditions on the controllability and observability grammians and their inverses, the solutions of the Riccati equations exist and converge exponentially as their initial time goes to — to give what we term -balancing solutions. The parameter has the interpretation of the gain of a differential equation. It determines the accuracy of the balancing transformation tracking and the exponential rate of convergence. Their exponentially convergent behavior ensures numerical robustness.Work partially supported by Boeing, and DSTO Australia.Visiting from Akita University, 1-1 Tegatagakuen-cho, Akita, 010, Japan.     

Internally balanced minimal realization of discrete SISO systems

Given the transfer function or the state equations in phase canonical form of a discrete SISO system, a method is proposed to obtain an internally balanced state-space representation of it.     

Identification/reduction to a balanced realization via the extendedimpulse response gramian

A new identification/reduction algorithm for linear, discrete time-invariant (LDTI) systems is proposed which is based on the extended impulse response gramian first defined here for LDTI systems. The reduction algorithm employs singular value decomposition to retain states corresponding to dominant singular values of these gramians. The proven properties of the reduced order models include convergence to a balanced realization with conditional controllability, observability, and asymptotic stability. A suboptimal property of the model (in minimizing an impulse response error norm) is also demonstrated. The proposed technique can handle impulse response data of deterministic or stochastic nature for system identification application     

A new algorithm for the minimal balanced realization of a transfer function matrix

A new algorithm is proposed here to obtain a minimal balanced realization directly from the transfer function matrix (TFM). This method which employs the singular-value decomposition (SVD) of an infinite block-Hankel matrix requires neither an initial minimal realization nor the solution of a Lyapunov matrix equation. The formulation is solely in terms of the coefficients of the transfer function matrix.     

Minimal realization of a differential system

There are many algorithms for deriving a state variable model for a system defined by a matrix transfer function. It is shown how these algorithms may be applied to the derivation of state variable models for systems defined by linear constant differential equations. without the use of polynomial computations.     

The general state-space model for a two-dimensional linear digital system

The general state-space model for a 2-D linear digital system is presented. A new definition of state-transition matrix is given. Based on the definition, it is easy to calculate the state-transition matrix for any linear digital system. The general response formula for a system follows simply from the definition. A new definition of the characteristic function of a system and a theorem parallel to the Cayley-Hamilton theorem are also given. The presented results apply to any linear causal system.     

Balanced realization of stable transfer function matrices

Simple formulas are presented to compute the internally balanced minimal realization and the singular decomposition of the Hankel operator of a given continuous-time p×m stable transfer function matrix E(s)/d(s). The proposed formulas involve the Schwarz numbers of d(s) and the singular eigenvalues-eigenmatrices of a suitable finite matrix. Similar results are also obtained for a given discrete-time transfer function matrix     

New algorithm for minimal balanced realization of transfer function matrix

A simple method for calculating the gramians of any stable realization using algebraic computation is described. This allows the development of a new algorithm to obtain a minimal balanced realization. The algorithm presented is shown to be computationally simpler and more efficient than previous methods and is illustrated by an example.     

A simple algorithm on minimal balanced realization for transferfunction matrices

Given a transfer function matrix, it is shown that its minimal balanced realization can be obtained directly from the singular values and the singular vectors of a constant matrix constructed from the coefficients of the least common denominator polynomial. The algorithm is based on the close relationship of controllability and the observability gramians to the singular value decomposition of the associated infinite block Hankel matrix     

Convergence and convergence rate of the balanced realization truncations for infinite-dimensional discrete-time systems

In this paper, we study approximation via balanced realizations for a large class of infinite-dimensional discrete-time linear systems. We give properties of the truncated system and prove that the approximation is L₂-convergent. In the case of nuclear systems, we prove convergence in nuclear norm and give an estimation of the L_∞-convergence rate.